bluuebunny/crossref_metadata_2025 huggingface dataset:
Dimensions of spaces of generalized spherical functions
Authors: Huang Jing-Song , Oshima Toshio , Wallach Nolan
Published: February 2007

Generalized spherical functions are defined to be joint eigenfunctions of some invariant differential operators with fixed K-type on both sides on a semisimple Lie group. One of our main results is the same dimension formula for all spaces of generalized spherical functions, which is independent of eigenvalues. The other main result is proof of the existence of a global basis for all spaces of generalized spherical functions, which is holomorphic in the parameter for the eigenvalues. As an application, we calculate the distribution characters of K-bi-finite eigenfunctions of the center of enveloping algebra for split groups.
Holomorphic curves omitting five planes in projective space
Authors: Eremenko Alexandre
Published: February 2007

In 1928 H. Cartan proved an extension of Montel's normality criterion to holomorphic curves in the complex projective plane P 2 . He also conjectured that a similar result is true for holomorphic curves in P n for any n . Recently, the author constructed a counterexample to this conjecture for any n ≥ 3. In this paper we show how to modify Cartan's conjecture so that it becomes true, at least for n = 3.
Acyclicity of the groups of homeomorphisms of the Menger compact spaces
Authors: Sergiescu Vlad , Tsuboi Takashi
Published: February 2007

Let μ k be the k -dimensional Menger compact space. We show that the group Homeo (μ k ) of homeomorphisms of μ k is acyclic.
Hecke algebras and harmonic analysis on p -adic groups
Authors: Reeder Mark
Published: February 2007

We compute Plancherel measures and formal degrees for unipotent representations of p -adic groups, using Hecke algebra isomorphisms. The results verify special cases of the conjectural uniformity of formal degrees in an L -packet.
Fundamental groups of complements to singular plane curves
Authors: Shimada Ichiro
Published: February 2007

The classical hyperplane section theorem of Zariski about the fundamental groups of the complements to hypersurfaces in the complex projective space is generalized to the weighted homogeneous case. Using this result, we study how the fundamental group of the complement to a projective plane curve changes under covering of the projective plane by another projective plane. We also give an example of plane curves whose complements have nonabelian and finite fundamental groups. Few examples of such curves have been known. By the weighted Zariski's hyperplane section theorem, we can determine the group structure of these finite nonabelian groups.
Local existence with minimal regularity for nonlinear wave equations
Authors: Zhou Yi
Published: February 2007

In this paper, we consider the Cauchy problem of semilinear wave equations which satisfy the "null condition." We prove that the problem is locally well-posed in H s +1 for s > ¾ in 1 + 3 dimensions and s > ¼ in 1 + 2 dimensions. Moreover, it is shown that the result in 1 + 2 dimensions is sharp.
On the Swan conductor in positive characteristic
Authors: Matsuda Shigeki
Published: February 2007

Let X be a proper smooth surface over an algebraically closed field of positive characteristic and U be a complement of a simple normal crossing divisor. For a smooth l -adic sheaf Ƒ on U , Deligne proved a formula calculating the Euler characteristic of Ƒ by local invariants. Kato gave another formula for the Euler characteristic in case where Ƒ is of rank 1, using class field theory. In this paper, we show that local terms of these formulas coincide, admitting certain conjectures for vanishing cycles.
Galois invariants for S -units
Authors: Gruenberg K. W. , Weiss A.
Published: February 2007

Let K / k be a finite Galois extension of number fields with Galois group G and let S be a finite G -stable set of primes of K , containing all primes which are archimedean or ramified over k and which generates the ideal class group. By Theorem B, the G -module E of S -units of K is determined, up to stable isomorphism, by (a) the [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] G -lattice Δ S , which is the kernel of the augmentation [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] S → [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /], (b) the G -module μ of roots of unity in K , (c) a distinguished character ε of H 2 ( G , Hom (Δ S , μ)), and (d) the Chinburg class Ω m ( K / k ) in the locally free class group of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /] G . Our method is a study of the homotopy properties of Tate sequences of K / k , hence it is essential that our Galois invariants be specified without prior knowledge of these sequences. This is clear for (a) and (b), while for (c) it follows from Theorem A, which expresses ε in terms of the local and global invariant maps of class field theory. And for (d), it would follow from Chinburg's conjecture that Ω m is the root number class of K / k .
The Brauer group of a locally compact groupoid
Authors: Kumjian Alexander , Muhly Paul S. , Renault Jean N. , Williams Dana P.
Published: February 2007

We define the Brauer group Br ( G ) of a locally compact groupoid G to be the set of Morita equivalence classes of pairs ( A , α) consisting of an elementary C *-bundle A over G (0) satisfying Fell's condition and an action α of G on A by *-isomorphisms. When G is the transformation groupoid X × H , then Br( G ) is the equivariant Brauer group Br H ( X ). In addition to proving that Br( G ) is a group, we prove three isomorphism results. First we show that if G and H are equivalent groupoids, then Br( G ) and Br( H ) are isomorphic. This generalizes the result that if G and H are groups acting freely and properly on a space X , say G on the left and H on the right, then Br G ( X / H ) and Br H ( G \ X ) are isomorphic. Secondly we show that the subgroup Br 0 ( G ) of Br ( G ) consisting of classes [ A , α] with A having trivial Dixmier-Douady invariant is isomorphic to a quotient ε ( G ) of the collection Tw ( G ) of twists over G . Finally we prove that Br( G ) is isomorphic to the inductive limit Ext( G , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]) of the groups ε( G X ) where X varies over all principal G spaces X and G X is the imprimitivity groupoid associated to X .
On the Galois structure of equivariant line bundles on curves
Authors: Agboola A. , Burns D.
Published: February 2007

Let k be a finite field, and let X be a smooth, projective curve over k with structure sheaf [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. Let G be a finite group, and write C1([inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /][G]) for the reduced Grothendieck group of the category of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /][ G ]-vector bundles. In this paper we describe explicitly the subgroup of C1([inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /][ G ]) which is generated by the classes arising from G -stable invertible sheaves on tame Galois covers of X which have Galois group G .
On Galois structure invariants associated to Tate motives
Authors: Burns D. , Flach M.
Published: February 2007

We establish the equivalence of two definitions of invariants measuring the Galois module structure of K-groups of rings of integers in number fields (due to Chinburg et al. on the one hand and the authors on the other). We also make some remarks concerning the possibility of yet another such definition via Lichtenbaum complexes.
Finiteness and tenseness theorems for Riemannian foliations
Authors: Domínguez Demetrio
Published: February 2007

We prove a finiteness theorem for the spectral sequence ( E i (∇), ( d ∇ ) i ) associated to a Riemannian foliation [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] on a compact manifold M , and to a flat vector bundle E over M with flat connection ∇. Using this result we prove that every Riemannian foliation on a compact manifold is tense (in the sense of [F. W. Kamber and Ph. Tondeur, Foliations and metrics, Progr. Math. , vol. 32, 1983, pp. 103-152]). We also show that the main tautness theorems for Riemannian foliations on compact manifolds, which were proved by several authors, are immediate consequences of our results.
Rational cohomology and cohomological stability in generic representation theory
Authors: Kuhn Nicholas J.
Published: February 2007

With F q a finite field of characteristic p , let [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]( q ) be the category whose objects are functors from finite dimensional F q -vector spaces to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]-vector spaces. Friedlander and Suslin have introduced a category [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] of "strict polynomial functors" which has the same relationship to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /]( q ) that the category of rational GL m -modules has to the category of GL m ( F q )-modules. Our main theorem says that, for all finite objects F, G ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="05i" /], and all s , the natural restriction map from [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="06i" /] ( F ( k ) , G ( k ) ) to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="07i" /] ( F, G ) is an isomorphism for all large enough k and q . Here F ( k ) denotes F twisted by the Frobenius k times. This combines with an analogous theorem of Cline, Parshall, Scott, and van der Kallen to show that, for all finite F, G ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="08i" /], and all s , evaluation on an m dimensional vector space V m induces an isomorphism from [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="09i" /] ( F, G ) to Ext s GL m ( F q ) ( F ( V m ), F ( V m )) for all large enough m and q . Thus group cohomology of the finite general linear groups has often been identified with MacLane (or Topological Hochschild) cohomology.
Singular Levi-flat real analytic hypersurfaces
Authors: Burns Daniel , Gong Xianghong
Published: February 2007

We initiate a systematic local study of singular Levi-flat real analytic hypersurfaces, concentrating on the simplest nontrivial case of quadratic singularities. We classify the possible tangent cones to such hypersurfaces and prove the existence and convergence of a rigid normal form in the case of generic (Morse) singularities. We also characterize when such a hypersurface is defined by the vanishing of the real part of a holomorphic function. The main technique is to control the behavior of the homorphic Segre varieties contained in such a hypersurface. Finally, we show that not every such singular hypersurface can be defined by the vanishing of the real part of a holomorphic or meromorphic function, and give a necessary condition for such a hypersurface to be equivalent to an algebraic one.
On the geometry of classifying spaces and horizontal slices
Authors: Lu Zhiqin
Published: February 2007

We study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let U be a neighborhood of the moduli space. Then we know the universal covering space V of U is a smooth manifold. Suppose D is the classifying space of a polarized Calabi-Yau manifold with the automorphism group G . Then we prove that the map from V to D induced by the period map is a pluriharmonic map. We also give a Kähler metric on V , which is called the Hodge metric. We prove that the Ricci curvature of the Hodge metric is negative away from zero. We also proved the nonexistence of the Kähler metric on the classifying space of a Calabi-Yau threefold which is invariant under a cocompact lattice of G .
Weyl asymptotics for the Laplacian on asymptotically Euclidean spaces
Authors: Christiansen T.
Published: February 2007

We prove a trace-type formula for the Laplacian on an asymptotically Euclidean space and use this to obtain Weyl asymptotics of the scattering phase. Other results include an explicit calculation of the leading order singularity of the scattering matrix and results on the behavior of the resolvent and scattering matrix near 0.
Integral points on subvarieties of semiabelian varieties, II
Authors: Vojta Paul
Published: February 2007

This paper proves a finiteness result for families of integral points on a semiabelian variety minus a divisor, generalizing the corresponding result of Faltings for abelian varieties. Combined with the main theorem of the first part of this paper, this gives a finiteness statement for integral points on a closed subvariety of a semiabelian variety, minus a divisor. In addition, the last two sections generalize some standard results on closed subvarieties of semiabelian varieties to the context of closed subvarieties minus divisors.
Limits of Galois representations in fundamental groups along maximal degeneration of marked curves, I
Authors: Nakamura Hiroaki
Published: February 2007

We study Gal[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-actions on the fundamental groups arising in deformation of maximally degenerate marked curves, and give explicit descriptions of them in terms of the principal parameters of the Grothendieck-Teichmüller group [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]. As a special application, we present Galois theoretic connections between the moduli spaces M 0,4 , M 0,5 , M 1,1 and M 1,2 which lead to a newtype equation satisfied by the image of Gal[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /].
Computing norms of free operators with matrix coefficients
Authors: Lehner Franz
Published: February 2007

Let g 1 , g 2 , . . . , g n be the generators of the free group F n and denote by λ its left regular representation. A formula for norms of operators of the form Σ a i ⊗ λ( g i ) where a i are complex matrices or operators is derived similarly to the formula of Akemann and Ostrand for the scalar case. This formula can be used to compute norms of arbitrary finitely supported convolution operators on the free group. Essentially the same technique yields a formula for the norms of sums of matrix valued creation and annihilation operators on full Fock space. Finally some results about the numerical evaluation of the formula are proved.
Residue calculus and effective Nullstellensatz
Authors: Berenstein Carlos A. , Yger Alain
Published: February 2007

Multivariate residue calculus (in the spirit of J. Lipman) is developed from the computational point of view (for example with several variants of the classical Transformation Law), and used in order to make totally explicit the Bézout identity (and therefore the algebraic Nullstellensatz) in K [ X 1 , . . . , X n ], where K is an infinite field of arbitrary characteristic. Such identities provide sharp size estimates for the denominator and the 'divisors" in the Bézout identity when K is the quotient field of a factorial regular ring A equipped with a size (such as Z or F p [τ 1 , . . . , τ q ]). The estimates obtained by the authors in a previous work in the case A = Z are sharpened here, while analytic techniques are replaced with an algebraic approach.
Adelic Chern forms and applications
Authors: Hübl Reinhold , Yekutieli Amnon
Published: February 2007

Let X be a variety over a field of characteristic 0. Given a vector bundle E on X we construct Chern forms c i ( E ;∇) ∈ Γ( X ,A 2 i X ). Here A · X is the sheaf of Beilinson adeles and ∇ is an adelic connection . When X is smooth H p Γ( X ,A · X ) = H p DR ( X ), the algebraic De Rham cohomology, and c i ( E ) = [ c i ( E ;∇)] are the usual Chern classes. We include three applications of the construction: (1) existence of adelic secondary (Chern-Simons) characteristic classes on any smooth X and any vector bundle E ; (2) proof of the Bott Residue Formula for a vector field action; and (3) proof of a Gauss-Bonnet Formula on the level of differential forms, namely in the De Rham-residue complex.
Toroidal and reductive Borel-Serre compactifications of locally symmetric spaces
Authors: Goresky Mark , Tai Yung-Sheng
Published: February 2007

By "Hermitian locally symmetric space" we mean an arithmetic quotient of a bounded symmetric domain. Both the toroidal and the reductive Borel-Serre compactifications of such a space come equipped with canonical mappings to the Baily-Borel Satake compactification. In this article we show that there is a mapping from the toroidal compactification to the reductive Borel-Serre compactification, whose composition with the projection to the Baily-Borel compactification agrees with the canonical projection up to an arbitrarily small homotopy. We also consider arithmetic quotients of a self-adjoint homogeneous cone. There is a canonical mapping from the reductive Borel-Serre compactification to the standard compactification of such a locally symmetric cone. We show that this projection, when restricted to the closure of a polyhedral cone, has contractible fibers.
Minimizing currents in open manifolds and the n - 1 homology of nonnegatively Ricci curved manifolds
Authors: Itokawa Yoe , Kobayashi Ryoichi
Published: February 2007

We first of all obtain a condition under which a homology class of a complete noncompact Riemannian manifold can be represented by an area-minimizing integral current. We then use this result to study the codimension 1 integral homology of complete noncompact Riemannian manifolds with nonnegative Ricci curvature. Specifically, we show the following two results. On one hand, if such an n dimensional manifold M has volume growth faster than 1, then the n - 1 homology group of M is trivial. If on the other hand the diameter growth of a similar M is bounded, then the n - 1 homology group is either trivial, Z , or Z 2 . We also offer other applications of the techniques developed for these theorems to both n - 1 homology groups and volume growth of minimal submanifolds in various complete noncompact Riemannian spaces.
Almost regular sequences and Betti numbers
Authors: Aramova Annetta , Herzog Jürgen
Published: February 2007

Let Δ be a simplicial complex, and Δ s the shifted simplicial complex of Δ, as defined by Kalai. It is shown that the Stanley-Reisner ideals I Δ and I Δ s have the same extremal Betti numbers. This theorem is the squarefree analogue of the corresponding result by Bayer, Charalambous and Popescu which asserts that a graded ideal and its generic ideal have the same extremal Betti numbers. Our theorem implies well-known results by Kalai according to which Δ and Δ s have the same simplicial homology, and Δ is Cohen-Macaulay if and only if its shifted complex is Cohen-Macaulay.
The Steinberg curve
Authors: Esnault Hélène , Levine Marc
Published: February 2007

Let E and E ' be elliptic curves over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. We construct non-torsion 0-cycles in the kernel of the Albanese mapping CH 0 ( E x E ') deg 0 → E x E ', which are not detectable by a certain class of cohomology theories, including the cohomology of the analytic motivic complex involving the dilogarithm function defined by S. Bloch. This is in contrast to the étale version of Bloch's complex defined by S. Lichtenbaum, which contains the Chow group.
Degeneration of l -adic weight spectral sequences
Authors: Nakayama Chikara
Published: February 2007

The degeneracy of the l -adic weight spectral sequence over any trait (with no assumptions on its residue field) is proved by the method of log geometry in the sense of Fontaine-Illusie.
Correction to "On the ABC conjecture and diophantine approximation by rational points"
Authors: Vojta Paul
Published: February 2007

This addendum corrects the attribution for some of the major results of P. Vojta, Amer. J. Math. 122 (2000), 843-872.
Mapping-class-group action versus Galois action on profinite fundamental groups
Authors: Matsumoto Makoto , Tamagawa Akio
Published: February 2007

Let X be an algebraic curve of genus g, n -punctured, defined over a number field K . Then, the profinite or the pro- l completion of the topological fundamental group of X admits two actions: the action of the profinite completion of the mapping class group of the orientable surface of topological type ( g, n ) and the action of the absolute Galois group of K . This paper compares these two. In the profinite case, it is shown that the intersection of the images of these two actions is trivial if X is affine and its fundamental group is nonabelian. On the contrary, in the pro- l case, there are many curves such that the image of the Galois action contains the image of the mapping-class-group action. It is proved that the set of points corresponding to such curves is dense in the moduli space of ( g, n )-curves.
On automorphisms of the Toeplitz algebra
Authors: Muhly Paul S. , Xia Jingbo
Published: February 2007

In this paper we completely determine those C *-automorphisms α of the full Toeplitz algebra which have the form [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] + compact operator, where σ is a bi-Lipschitz homeomorphism of the unit circle.
Sobolev algebras on Lie groups and Riemannian manifolds
Authors: Coulhon Thierry , Russ Emmanuel , Tardivel-Nachef Valérie
Published: February 2007

We prove that on any connected unimodular Lie group G , the space L p α (G) ∩ L ∞ (G), where L p α (G) is the Sobolev space of order α > 0 associated with a sublaplacian, is an algebra under pointwise product. This generalizes results due to Strichartz (in the Euclidean case), to Bohnke (in the case of stratified groups), and others. A global version of this fact holds for groups with polynomial growth. We give similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.
The dimension of the leafwise reduced cohomology
Authors: Álvarez López Jesús A. , Hector Gilbert
Published: February 2007

Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, especially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations with "appropriate coefficients." The leafwise reduced cohomology is also described for homogeneous foliations with dense leaves on closed nilmanifolds.
Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
Authors: Tao Terence
Published: February 2007

The X s,b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behavior of nonlinear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in terms of the L 2 norms of the component functions. In this paper we systematically study weighted convolution estimates on L 2 . As a consequence we obtain sharp bilinear estimates for the KdV, wave, and Schrödinger X s,b spaces.
The topological Rohlin property and topological entropy
Authors: Glasner Eli , Weiss Benjamin
Published: February 2007

For a compact metric space X let G = H ( X ) denote the group of self homeomorphisms with the topology of uniform convergence. The group G acts on itself by conjugation and we say that X satisfies the topological Rohlin property if this action has dense orbits. We show that the Hilbert cube, the Cantor set and, with a slight modification, also even dimensional spheres, satisfy this property. We also show that zero entropy is generic for homeomorphisms of the Cantor set, whereas it is infinite entropy which is generic for homeomorphisms of cubes of dimension d ≥ 2 and the Hilbert cube.
A compactness property for solutions of the Ricci flow on orbifolds
Authors: Lu Peng
Published: February 2007

In this paper we consider Ricci flow on orbifolds with at most isolated singularities. We generalize two results of R. Hamilton to orbifolds. The first result is the compactness property of Ricci flow and the second is an injectivity radius estimate for Ricci flow. In the proof of the compactness property we give an orbifold version of the injectivity radius estimate of J. Cheeger, M. Gromov and M. Taylor. Also along the way we prove a compactness property of Riemannian orbifolds.
Complete modules and torsion modules
Authors: Dwyer W. G. , Greenlees J. P. C.
Published: February 2007

Suppose that R is a ring and that A is a chain complex over R . Inside the derived category of differential graded R -modules there are naturally defined subcategories of A -torsion objects and of A -complete objects. Under a finiteness condition on A , we develop a Morita theory for these subcategories, find conceptual interpretations for some associated algebraic functors, and, in appropriate commutative situations, identify the associated functors as local homology or local cohomology. Some of the results are suprising even in the case R = [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] and A = [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /].
Properties of harmonic measures in the Dirichlet problem for nilpotent Lie groups of Heisenberg type
Authors: Capogna Luca , Garofalo Nicola , Nhieu Duy-Minh
Published: February 2007

In groups of Heisenberg type we introduce a large class of domains, which we call ADP, admissible for the Dirichlet problem , and we prove that on the boundary of such domains, harmonic measure, ordinary surface measure, and the perimeter measure, are mutually absolutely continuous. We also establish the solvability of the Dirichlet problem when the boundary datum belongs to L p , 1 < p ≤ ∞, with respect to the ordinary surface measure. Here, the harmonic measure is that relative to a sub-Laplacian associated with a basis of the first layer of the Lie algebra. A domain is called ADP if it is a nontangentially accessible domain and it satisfies an intrinsic outer ball condition.
Deformations of the trivial line bundle and vanishing theorems
Authors: Clemens Herbert , Hacon Christopher
Published: February 2007

This paper reproves a general form of the Green-Lazarsfeld "generic vanishing" theorem and more recent strengthenings, as well as giving some new applications.
The representation of integers as sums of squares
Authors: Shimura Goro
Published: February 2007

We present a uniform method by which we obtain an explicit formula for the number of representations of an integer as the sum of n squares for each n in the range 2 ≤ n ≤ 8. The final formulas for odd n are new, though those for even n are not. We also present a formula for the dominant term for the number for an arbitrary n .
Volumes of complex analytic subvarieties of Hermitian symmetric spaces
Authors: Hwang Jun-Muk , To Wing-Keung
Published: February 2007

We give lower bounds of volumes of k -dimensional complex analytic subvarieties of certain naturally defined domains in n -dimensional complex space forms of constant (positive, zero, or negative) holomorphic sectional curvature. For each 1 ≤ k ≤ n , the lower bounds are sharp in the sense that these bounds are attained by k -dimensional complete totally geodesic complex submanifolds. Such lower bounds are obtained by constructing singular potential functions corresponding to blow-ups of the Kähler metrics involved. Similar lower bounds are also obtained in the case of Hermitian symmetric spaces of noncompact type. In this case, the lower bounds are sharp for those values of k at which the Hermitian symmetric space contains k -dimensional complete totally geodesic complex submanifolds which are complex hyperbolic spaces of minimum holomorphic sectional curvature.
Upper semicontinuity of the dimensions of automorphism groups of domains in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]
Authors: Fridman Buma L. , Ma Daowei , Poletsky Evgeny A.
Published: February 2007

Let [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] be the metric space of all bounded domains in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] with the metric equal to the Hausdorff distance between boundaries of domains. We prove that the dimension of the group of automorphisms of domains is an upper semicontinuous function on [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /]. We also provide theorems and examples regarding the change in topological structure of these groups under small perturbation of a domain in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="05i" /].
Generalized Whittaker models and the Bernstein center
Authors: Bushnell Colin J. , Henniart Guy
Published: February 2007

Let F be a non-Archimedean local field and G the group of F -points of a connected reductive algebraic group defined over F . Let B be a minimal F -parabolic subgroup of G with Levi component T and unipotent radical U . We let ξ be a smooth character of U, nondegenerate in a certain sense. We consider the theory of smooth ξ-Whittaker functions on G via the structure of the representation c -Ind ξ of G which is compactly induced by ξ. We prove a finiteness result for these generalized Whittaker models, corresponding to the uniqueness property for classical Whittaker models on quasi-split groups. In many cases, including the one where G is quasi-split, we describe the ring of G -endomorphisms of c -Ind ξ in terms of the Bernstein Center. This has consequences for the structure of the category of smooth representations of G . It gives an algebraic technique for finding improved (and more general) versions of results on classical Whittaker functions originally obtained by more analytic methods.
An E ∞ splitting of spin bordism
Authors: Laures Gerd
Published: February 2007

The work determines the E ∞ structure of the K (1)-local spin bordism spectrum by giving a multiplicative splitting into E ∞ cells. The splitting leads to a cellular decomposition of the Â -map and creates new isomorphisms of Conner-Floyd type.
On a general Thue's equation
Authors: Corvaja Pietro , Zannier Umberto
Published: February 2007

We analyze the integral points on varieties defined by one equation of the form f 1 · · · f r = g , where the f i , g are polynomials in n variables with algebraic coefficients, and g has "small" degree; we shall use a method that we recently introduced in the context of Siegel's Theorem for integral points on curves. Classical, very particular, instances of our equations arise, e.g., in a well-known corollary of Roth's Theorem (the case n = 2, f i linear forms, deg g < r -2) and with the norm-form equations , treated by W. M. Schmidt. Here we shall prove (Thm. 1) that the integral points are not Zariski-dense, provided Σdeg f i > n · max (deg f i ) + deg g and provided the f i , g , satisfy certain (mild) assumptions which are "generically" verified. Our conclusions also cover certain complete-intersection subvarieties of our hypersurface (Thm. 2). Finally, we shall prove (Thm. 3) an analogue of the Schmidt's Subspace Theorem for arbitrary polynomials in place of linear forms.
Equivalences of derived catgories of sheaves on smooth stacks
Authors: Kawamata Yujiro
Published: February 2007

We extend Orlov's representability theorem on the equivalence of derived categories of sheaves to the case of smooth stacks associated to normal projective varieties with only quotient singularities.
Cosimplicial objects and little n -cubes, I
Authors: McClure James E. , Smith Jeffrey H.
Published: February 2007

In this paper we show that if a cosimplicial space has a certain kind of combinatorial structure then its total space has an action of an operad weakly equivalent to the little n -cubes operad. Our results are also valid for cosimplicial spectra.
How (Not) to Look at a Woman: Bodily Encounters and the Failure of the Gaze in Horace's C. 1.19
Authors: Sutherland Elizabeth H. (Elizabeth Hamilton)
Published: February 2007

Like the lovers of Roman elegy, the speaker of
C. 1.19 claims to be dominated by his beloved. As in elegy,
however, this "inversion" is a sham. The speaker retains control over his
beloved while expressing his secret hostility toward her. Associating
Glycera's body with toxic, uncontrolled nature, the lover claims that
he risks harm simply by gazing upon her. He attempts to control his
unruly object of desire by identifying her as material for his poetry,
by immobilizing her as a statue, and by symbolically killing/penetrating
her in the ode's closing sacrifice.
Agamemnon's Test of the Army in Iliad Book 2 and the Function of Homeric akhos
Authors: Cook Erwin F.
Published: February 2007

I offer a reading of the Diapeira episode based
on the semantics and thematics of akhos. My findings resolve a
crux at 2.171, where Homer identifies akhos as the reason
Odysseus is not launching his ship. Homer clearly signposts the nature
of Odysseus' akhos as grief over loss of time
in Athene's subsequent speech to him, but the reference is proleptic
and has consequently eluded the commentators.
The Hands of Death: Ovid Amores 3.9.20
Authors: Williams Frederick
Published: February 2007

This article examines Ovid Amores 3.9, the elegy
on the death of Tibullus, and especially its allusions to Tibullus' own
poetry and its pervasive use of religious vocabulary and imagery. It
focuses on the phrase obscuras. . . manus, the transmitted
reading in line 20, and reveals a significant allusion to Callimachus,
ep. 2 Pf. (also on the death of a friend and fellow-poet). Current
interpretations of obscuras are considered and found inadequate
to the context and tenor of the poem; the very slight change of only
two letters is proposed to yield the adjective obscenas, a highly
charged word with religious associations.
Control of Costume in Three Plays of Aristophanes
Authors: Compton-Engle Gwendolyn
Published: February 2007

This paper examines the manipulation of costume by characters in
Aristophanes' Acharnians, Thesmophoriazusae, and Frogs. Costume
control is viewed as a type of comic competition. In Acharnians,
Dicaeopolis' overall mastery is expressed by his control over costume; in
Thesmophoriazusae, the Relative experiences a series of costume-related
humiliations; in Frogs, Dionysus and Xanthias exchange costume, reducing
Dionysus' status. Successful manipulation of costume is associated with
masculinity and heightened status, while failure to control costume is
correlated with emasculation and lowered status. Characters' handling
of costume has additional reference to the poet's degree of mastery
over the elements of dramatic production.
Satire in Green: Marked Clothing and the Technique of indignatio at Juvenal 5.141-45
Authors: Hopman Marianne
Published: February 2007

At Juvenal 5.141-45, Virro distributes a curious series of
presents to the children of his impoverished client Trebius: a viridis
thorax, nuts, and an as. Through an exploration of the connotations
attached to these gifts, I argue that the scene provides a vivid mise en
abyme for the rest of the poem. Just as the dinner offered to Trebius is
not only meager but transforms him into a buffoon, the presents given
to his children are both mean and perverse. In particular, the viridis
thorax has un-Roman and effeminate connotations akin to the description
of patronage as a sexual perversion in Satire 9.
Centaurs in Love and War: Cyllarus and Hylonome in Ovid Metamporphoses 12.393-428
Authors: Debrohun Jeri Blair
Published: February 2007

This article provides a close reading of Ovid's ecphrastic depiction of two Centaur lovers and their ideally mutual relationship, an episode that serves as a digression in the midst of Nestor's narration of the Battle of the Lapiths and Centaurs in Met. 12. Ovid uses allusions to two didactic poems, Lucretius' De Rerum Natura and Ovid's own Ars Amatoria III, as he explores in the Cyllarus-Hylonome interlude both hybridity itself and the relationships and possible combinations of a number of conceptual opposites: natura and cultus, human and animal, male and female, love and war, and the contrasting values of lyric-elegiac and epic poetry. A final section discusses how the issues explored within the digression reflect a concern with similar issues in the wider context of Book 12 and of the Metamorphoses as a whole.
Marriage, Identity, and the Tale of Mestra in the Hesiodic Catalogue of Women
Authors: Ormand Kirk
Published: February 2007

Fragment 43a of the Hesiodic Catalogue of Women tells the lively tale of Mestra, a female shape-shifter who supports her father through serial marriages. I argue that this narrative demonstrates a typical mythic pattern, in which female shape-shifting is both a method of avoiding marriage and emblematic of an unmarried woman's unstable social position. I argue further that this version of Mestra's story in particular represents an attempt to mediate a question that was becoming increasingly important in sixth-century Athens, namely: to which household does a bride belong, her father's or her husband's?
Homecoming, Immigration, and the National Ethos: Russian-Jewish Homecomers Reading Zionism
Authors: Lomsky-Feder Edna , Rapoport Tamar
Published: February 2007

For immigrants entering a society characterized by a strong national ethos of homecoming, the interpretation of that ethos is essential to their making sense of their new lives and reconstructing their identity. Our case study explores how immigrants interpret the Israeli national ethos while struggling over their position in the old-new homeland. Analyzing personal narratives of Russian-Jewish university students in Israeli society, we discuss how their multivocal critiques of the "national-Zionist ethos" reflect and fuel the heated and dividing discourse over national identity in Israeli society of the 1990s. We explain how the homecomers read the national ethos, confront it, and participate in the local cultural discourse by their dual position as outsiders-insiders in the new society, together with their experiences as a diasporic minority group in the native land. We suggest that the interaction between two cultural systems-the Diasporic heritage of the Jewish Russian homecomers and the Zionist ethos-broadens and elaborates the Israeli national discourse. [national ethos, homecoming, immigration, personal narrative, Israeli society]
"Like Nixon Coming to China": Finding Common Ground in a Multi-Ethnic Coalition for Environmental Justice
Authors: Checker Melissa
Published: February 2007

This article uses ethnographic fieldwork to illustrate how a multi-ethnic group of activists in Brooklyn, New York, formed a coalition for environmental justice in thhborhood. Until the late 1980s local activists had organized in separate and antagonistic movements, competing over access to housing, schools, and police protection. However, as they increasingly realized that the environment was an urban concern, and was subject to discrimination, activists added it to their organizing agendas. In so doing, activists began to construct an expansive environmental narrative that cast all minorities in the neighborhood as united in the face of disproportionately high pollution rates. Activists thus found that they could enhance their environmental struggles by creating environmental identities that superseded rigidly defined identities based on ethnicity. Through organizing for environmental justice, activists redefined the meaning and significance of ethnic differences. [ethnicity, environmental justice, social movements, urban United States]
"Environmental Conflict" and the Social Life of Environmental Security Discourse
Authors: Timura Christopher T.
Published: February 2007

The concept "environmental conflict" has enjoyed increasing popularity within environmental discourses, both as a focal point of interdisciplinary research efforts and as a buzzword within general discussions concerning international security both in the U.S. and Europe. Though the concept has become a part the "master narrative" of environmentalism, its uncritical application to conflict settings has the potential to misdirect the attention of conflict mediators and policy makers. In this article the author traces the contours of environmental security discourse, while critiquing environmental conflict models. Highlighting a comparative study of three resource-related outbreaks of collective violence, the author finds that in none of the cases compared—neither the Zapatista Rebellion of Chiapas, Mexico, the massacre at Eldorado dos Carajas, in Para, Brazil, nor the "Guinea Fowl" War of Northern Region, Ghana—can simple resource scarcity be implicated as a cause of violence. In contrast to current anthropological understandings of resource-related violence, environmental conflict models are unable to take into account the social and cultural nature of resource conflicts, including the roles that social histories, symbolically-mediated perception, and local political economies play in the outbreak of violence. Given both its inadequacies and policy importance, anthropologists could make useful interventions as participants in the developing environmental security discourse. [discourse, environmentalism, violence, environmental conflict, political ecology]
Negotiated and Mediated Meanings: Ethnicity and Politics in Israeli Newspapers
Authors: Lefkowitz Daniel
Published: February 2007

In this article the author explores the ways in which the media articulate discursive structure and lived experience through an analysis of the coverage of the 1999 Israeli national elections in one Israeli newspaper. Recent changes in Israeli electoral law unleashed new social forces that granted major political influence to ethnic parties. The renewed salience of (Jewish) ethnicity clashes, however, with dominant discourses of national identity, according to which a unitary Israeli identity subsumes particularistic Jewish ethnicities, while silencing Palestinian identity. Such changes imply an important role for the Israeli media, which has traditionally marked identity difference through distinct regimes for the expression and control of affect. The author examines constructions of affect, and their inscription onto particular social identities, in Yediot Ahronot , Israel's widest-circulation daily.
The Music of the Bahian Caboclos
Authors: Brazeal Brian
Published: February 2007

The Caboclos are a pantheon of deities worshipped in the
Candombl�s of Bahia and throughout Brazil. They are Brazilian
cowboys and Indians f�ted at public parties and private ceremonies
and invoked by devotees to work on earth. The incorporation of this
pantheon was enabled by the pragmatic efficacy attributed to music in
ritual contexts of Candombl� worship. In these ceremonies, music
is not just an accompaniment to ritual actions; it is the means by which
ritual work is done. This pragmatic efficacy creates the conditions of
possibility for innovation and incorporation of new gods and new ritual
practices.
The Slave and Freedman Personnel of Public Libraries in Ancient Rome
Authors: Houston George W
Published: February 2007

The lower-level personnel in Roman public
libraries of the early Empire were part of the emperor's domestic staff,
just as they had been household slaves in late Republican libraries. This
observation carries important implications. The book collections, at
least in origin, were the emperor's private possessions, not public
services like the roads, and he might closely control their use. His
slave vilici, not equestrian procurators, ordinarily directed
the daily work of the staff, and the commissioners of all the libraries
(originally Greek intellectuals, and not always procurators) may have
served primarily as scholarly advisers. No evidence supports the idea
of a centralized library administration.
Social Science History, Cultural History, and the Amnesty of 403
Authors: Ober Josiah
Published: February 2007

Response to a set of papers on the Athenian Amnesty of 403
b.c.
Lysias 18 and Athenian Memory of Civil War
Authors: Wolpert Andrew
Published: February 2007

Attempts to explain the success of the Athenian reconciliation
in 403 b.c.e. are easily frustrated because the evidence
is incomplete and because the conditions of postwar Athens were not
exceptional. Peace was not imposed on the Athenians through rules
and regulations; rather, it was constructed in civic discourse. The
Athenian reconciliation can, therefore, be better appreciated if studied
as a cultural construct that was ultimately negotiated on the plane of
ideology. Using Lysias 18 as a case study, the author shows how civil
war confounded the identity of Athenian citizens. Although discursive
analysis cannot explain why the Athenians avoided further civil war, it
does allow us to contextualize the disputes of the restored democracy,
to appreciate how Athenians remembered defeat and civil war, and to
understand how the past either united or divided them.
Her Turn to Cry: The Politics of Weeping in Roman Love Elegy
Authors: James Sharon L
Published: February 2007

Roman love elegy presents its male speakers as
weeping helplessly for a cruel mistress, the dura puella. Though
this image has dominated the reception of elegy, Ovid's Ars
amatoria and Amores deviate strikingly: in these works the
lover seeks to see his mistress weep. Further review demonstrates the same
desire, well hidden, in the elegies of Propertius and Tibullus. This
paper argues that Ovid shows the resentment underlying the elegiac
lover's tears, along with the desire for revenge in the form of his
beloved's compensatory tears.
Heraclitus the Paradoxographer: Peri Apiston, On Unbelieveable Tales
Authors: Stern Jacob
Published: February 2007

The text of Heraclitus the Paradoxographer
(so LSJ, although "Mythographer" would be better), which is here
translated with Introduction and Commentary, survives to the present in a
single 13th-century manuscript. Of the author nothing is known, although
he appears to belong to the late 1st or 2nd century A.D.
The text includes 39 items in which familiar myths are briefly told
and then interpreted through rationalism, euhemerism, allegory, or
etymology. Among extant mythographical collections this text is of
particular interest precisely because it exemplifies in brief compass
such a range of ancient strategies for the interpretation of myth.
Conversing with Ourselves: Canon, Freedom, Jazz
Authors: Kodat Catherine Gunther
Published: February 2007

Theodor Adorno's essay "On Jazz" is usually condemned as an elitist, if not racist, diatribe against jazz's possibility of attaining the status of "art" music. Adorno's concern with the ideological uses of jazz music, however, remains useful, particularly in light of recent efforts to claim a "high" art status for jazz through the creation of a canon. Ken Burns's recent PBS documentary Jazz vividly illustrates the problems with a "canonical" approach to jazz history, especially in its partial and awkward treatment of the anti-commercial free jazz movement. An understanding of jazz's double relationship to art and commerce gives unique insight into the complexity of the issue of canon formation generally.
From Spirituals to Swing: Sister Rosetta Tharpe and Gospel Crossover
Authors: Wald Gayle
Published: February 2007

Rosetta Tharpe was gospel music's first national star, one of its earliest recording artists, and its pre-eminent crossover figure of the 1940s, the decade of gospel's emergence as "popular" music. Such popularization of gospel held special significance for Tharpe as an African American female musician who negotiated the different modes of femininity available to her as, alternately, a popular or gospel entertainer. Although Tharpe earned scorn in some quarters for making music that confused the sacred/secular division, she took pleasure in, and found agency through, a constant shuttling between spheres.