subdivisions and local h vectors in part i a general theory of f vectors of simplicial subdivisions or triangulations of simplicial complexes is developed based on the concept of lo cal h vector as an application we prove that the h vector of a cohen macaulay complex increases under quasi geometric subdivision thus establishing a spe cial case of a conjecture of kalai and this author techniques include com mutative algebra homological algebra and the intersection homology of toric varieties in part ii we extend the work of part i to more general situations first a formal generalization of subdivision is given based on incidence alge bras special cases are then developed in particular one based on subdivisions of eulerian posets and involving generalized h vectors other cases deal with kazhdan lusztig polynomials ehrhart polynomials and a q analogue of eule rian posets many applications and examples are given throughout department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address rstan math mit edu this content downloaded from 157 55 39 210 on sat 30 jul 2016 05 59 16 utc all use subject to http about jstor org terms

symmetries of lagrangian fibrations abstract we construct fiber preserving anti symplectic involutions for a large class of symplectic manifolds with lagrangian torus fibrations in particular we treat the k3 surface and the six dimensional examples constructed by castano bernard and matessi 2009 8 which include a six dimensional symplectic manifold homeomorphic to the quintic threefold we interpret our results as corroboration of the view that in homological mirror symmetry an anti symplectic involution is the mirror of duality in the same setting we construct fiber preserving symplectomorphisms that can be interpreted as the mirror to twisting by a holomorphic line bundle

stratifiable maps and topological invariants let x and y be spaces and f x y be a map between them then a large family of problems in topology and geometry involve the attempt to relate the invariants of x and y via f this attempt has been successful often for the case x and y manifolds and f the projection of a fibre bundle for many types of important invariants for example the result of chernhirzebruch serre chs asserts that for y simply connected the signature of x is the product of the signatures of y and of the fibre f 1 y in this paper we undertake the study of maps in which the fiber may vary from point to point the spaces x and y will be any whitney stratified spaces with even codimension strata e g algebraic varieties and f will be a stratified map this means essentially that for v a component of a stratum of y thus v is an open manifold f 1v is a union of strata of x and the restriction of f to f71v is a locally trivial fibre bundle for example subanalytic maps of subanalytic sets can be stratified with respect to whitney

equivariant constructible koszul duality for dual toric varieties abstract for affine toric varieties x and x defined by dual cones we define an equivalence of categories between mixed versions of the equivariant derived category d t b x and the derived category of sheaves on x which are locally constant with unipotent monodromy on each orbit this equivalence satisfies the koszul duality formalism of beilinson ginzburg and soergel

enumeration of points lines planes etc one of the earliest results in enumerative combinatorial geometry is the following theorem of de bruijn and erd s every set of points e in a projective plane determines at least lvert e rvert lines unless all the points are contained in a line the result was extended to higher dimensions by motzkin and others who showed that every set of points e in a projective space determines at least lvert e rvert hyperplanes unless all the points are contained in a hyperplane let e be a spanning subset of an r dimensional vector space we show that in the partially ordered set of subspaces spanned by subsets of e there are at least as many r p dimensional subspaces as there are p dimensional subspaces for every p at most frac 1 2 r this confirms the top heavy conjecture by dowling and wilson for all matroids realizable over some field the proof relies on the decomposition theorem package for ell adic intersection complexes

generalized hypergeometric functions and rational curves on calabi yau complete intersections in toric varieties we formulate general conjectures about the relationship between the a model connection on the cohomology of ad dimensional calabi yau complete intersectionv ofr hypersurfacesv1 vr in a toric varietyp and the system of differential operators annihilating the special generalized hypergeometric series 0 constructed from the fan using this generalized hypergeometric series we propose conjectural mirrorsv ofv and the canonicalq coordinates on the moduli spaces of calabi yau manifolds

on the choice of outlet boundary conditions for patient specific analysis of aortic flow using computational fluid dynamics boundary conditions bcs are an essential part in computational fluid dynamics cfd simulations of blood flow in large arteries although several studies have investigated the influence of bcs on predicted flow patterns and hemodynamic wall parameters in various arterial models there is a lack of comprehensive assessment of outlet bcs for patient specific analysis of aortic flow in this study five different sets of outlet bcs were tested and compared using a subject specific model of a normal aorta phase contrast magnetic resonance imaging pc mri was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition computational results obtained with different outlet bcs were assessed in terms of their agreement with the pc mri velocity data and key hemodynamic parameters such as pressure and flow waveforms and wall shear stress related indices our results showed that the best overall performance was achieved by using a well tuned three element windkessel model at all model outlets which not only gave a good agreement with in vivo flow data but also produced physiological pressure waveforms and values on the other hand opening outlet bcs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features

a comparison of pilot aided channel estimation methods for ofdm systems this paper deals with the estimation of the channel impulse response cir in orthogonal frequency division multiplexed ofdm systems in particular we focus on two pilot aided schemes the maximum likelihood estimator mle and the bayesian minimum mean square error estimator mmsee the advantage of the former is that it is simpler to implement as it needs no information on the channel statistics on the other hand the mmsee is expected to have better performance as it exploits prior information about the channel theoretical analysis and computer simulations are used in the comparisons at snr values of practical interest the two schemes are found to exhibit nearly equal performance provided that the number of pilot tones is sufficiently greater than the cirs length otherwise the mmsee is superior in any case the mmsee is more complex to implement

conformal blocks and generalized theta functions let yp be the moduli space of rank r vector bundles with trivial determinant on a riemann surface x this space carries a natural line bundle the determinant line bundle s we describe a canonical isomorphism of the space of global sections of sk with the space of conformal blocks defined in terms of representations of the lie algebra 5 c z it follows in particular that the dimension of h yk is given by the verlinde formula

on the homology of the hilbert scheme of points in the plane geir ellingsrud 1 and stein arild stromme 2 i matematisk institutt universitetet i oslo blindern n oslo 3 norway 2 matematisk institutt universitetet i bergen n 5014 bergen norway although several authors have been interested in the hilbert scheme hilba ip z parametrizing finite subschemes of length d in the projective plane i1 i2 f 1 f2 br among others not much is known about the topological properties of this space the picard group has been calculated i f2 and the homology groups of hilb3 ip 2 have been computed hi in this paper we give a precise description of the additive structure of the homology of hilba ip2 applying the results of birula bialynicki b1 b2 on the cellular decompositions de fined by a torus action to the natural action of a maximal torus of sl 3 on hilbe ipz a rather easy consequence of the fact that this action has finitely many fixpoints is that the cycle maps between the chow groups and the homology groups are isomorphisms in particular there is no odd homology and the homology groups are all free the main objective of this work is to compute their ranks the betti numbers of hilba ipz as a byproduct of our method we get similar results on the homology of the punctual hilbert scheme and of the hilbert scheme of points in the affine plane it seems natural to generalize our results to any toric smooth surface however we give the results only for the rational ruled surfaces if with an indication of the necessary changes in the proofs for simplicity we work over the field of complex numbers but with an appropriate interpretation of the word homology our results remain valid over any base field

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

the douady space of a complex surface abstract we prove that a standard realization of the direct image complex via the so called douady barlet hilbert chow in the algebraic case morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi isomorphism of complexes this is a more precise form of a special case of the decomposition theorems of beilinson bernstein deligne gabber and m saito of which the proof we present is independent in addition it is elementary and transparent and does not use either perverse sheaves the methods of positive characteristic nor saito s theory of mixed hodge modules the proof hinges on the special case of the bi disk in the complex affine plane where we make explicit use of a construction of nakajima s and of the corresponding representation theoretic interpretation foreseen by vafa and witten some consequences of the decomposition theorem the gottsche formula holds for complex surfaces interpretation of the rational cohomologies of douady spaces as a kind of fock space new proofs of results of briancon and ellingsrud and stromme on punctual hilbert schemes and computation of the mixed hodge structure of the douady spaces in the kahler case we also derive a natural connection with equivariant k theory for which in the case of algebraic surfaces bezrukavnikov and ginzburg have proposed a different approach

construction of central elements in the affine hecke algebra via nearby cycles 0 1 overview let g be a connected reductive group over a finite field fq and let g k be the corresponding group over the local field k fq t let g o g k be a maximal compact subgroup of g k here o fq t and let hsph denote the hecke algebra of g k with respect to g o in other words hsph as a vector space consists of compactly supported bi g o invariant functions g k q and the product is defined by

lifting inequalities for polytopes we present a method of lifting linear inequalities for the flag f vector of polytopes to higher dimensions known inequalities that can be lifted using this technique are the non negativity of the toric g vector and that the simplex minimizes the cd index we obtain new inequalities for six dimensional polytopes in the last section we present the currently best known inequalities for dimensions 5 through 8

on simple polytopes letp be a simpled polytope ind dimensional euclidean space mathbb e d and let p be the subalgebra of the polytope algebra generated by the classes of summands ofp it is shown that the dimensions of the weight spaces r p of p are theh numbers ofp which describe the dehn sommerville equations between the numbers of faces ofp and reflect the duality between r p and d r p moreover p admits a lefschetz decomposition under multiplication by the element of 1 p corresponding top itself which yields a proof of the necessity of mcmullen s conditions in theg theorem on thef vectors of simple polytopes the lefschetz decomposition is closely connected with the new hodge riemann minkowski quadratic inequalities between mixed volumes which generalize minkowski s second inequality also proved are analogous generalizations of the aleksandrov fenchel inequalities a striking feature is that these are obtained without using brunn minkowski theory indeed the brunn minkowski theorem without characterization of the cases of equality can be deduced from them the connexion found between p and the face ring of the dual simplicial polytopep enables this ring to be looked at in two ways and a conjectured formulation of theg theorem in terms of a gale diagram ofp is also established

mixed hodge complexes on algebraic varieties using the theory of mixed hodge modules we introduce the notion of mixed hodge complex on an algebraic variety and establish the relation between the filtered complex of du bois and the corresponding complex of mixed hodge modules some application to the du bois singularity is given

koszul duality for toric varieties we show that certain categories of perverse sheaves on affine toric varieties x and x v defined by dual cones are koszul dual in the sense of beilinson ginzburg and soergel 1996 the functor expressing this duality is constructed explicitly by using a combinatorial model for mixed sheaves on toric varieties

weights of twisted exponential sums let k be a finite field of characteristic p l a prime number different from p psi k to overline bf q l ast a nontrivial additive character and chi k ast n to overline bf q l ast a character on k ast n then defines an artin schreier sheaf mathcal l psi on the affine line bf a k 1 and defines a kummer sheaf mathcal k chi on the n dimensional torus bf t k n let f in k x 1 x 1 1 ldots x n x n 1 be a laurent polynomial it defines a k morphism f bf t k n to bf a k 1 in this paper we calculate the weights of h c i bf t bar k n mathcal k chi otimes f ast mathcal l psi under some non degeneracy conditions on f our results can be used to estimate sums of the form sum x 1 ldots x n in k ast chi 1 f 1 x 1 ldots x n cdots chi m f m x 1 ldots x n psi f x 1 ldots x n where chi 1 ldots chi m k ast to bf c ast are multiplicative characters psi k to bf c ast is a nontrivial additive character and f1 fm f are laurent polynomials

heisenberg algebra and hilbert schemes of points on projective surfaces the purpose of this paper is to throw a bridge between two seemingly unrelated subjects one is the hilbert scheme of points on projective surfaces which has been intensively studied by various people see e g i br es g61 g62 the other is the infinite dimensional heisenberg algebra which is closely related to affine lie algebras see e g k we shall construct a representation of the heisenberg algebra on the homology group of the hilbert scheme in other words the homology group will become a fock space the basic idea is to introduce certain correspondences in the product of the hilbert scheme then they define operators on the homology group by a well known procedure they give generators of the heisenberg algebra and the only thing we must check is that they satisfy the defining relation here we remark that the components of the hilbert scheme are parameterized by numbers of points and our representation will be constructed on the direct sum of homology groups of all components our correspondences live in the product of the different components thus it is quite essential to study all components together our construction has the same spirit as the author s construction nal na4 of representations of affine lie algebras on homology groups of moduli spaces of instantons 1 on ale spaces which are minimal resolutions of simple singularities certain correspondences called hecke correspondences were used to define operators these twist instantons along curves irreducible components of the exceptional set while ours twist ideals around points in fact the hilbert scheme of points can be considered as the moduli space of rank 1 vector bundles or more precisely torsion free sheaves our construction should be considered as a first step to extend nal na4 to general 4 manifolds the same program was also proposed by ginzburg kapranov and vasserot gkv

the decomposition theorem perverse sheaves and the topology of algebraic maps we give a motivated introduction to the theory of perverse sheaves culminating in the decomposition theorem of beilinson bernstein deligne and gabber a goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties while most proofs are omitted we discuss several approaches to the decomposition theorem indicate some important applications and examples

exponential sums and newton polyhedra cohomology and estimates the basic objects of this study are exponential sums on a variety defined over a finite field fq q pa p char fq as we have remarked in some earlier articles 1 2 we find it more natural to begin with exponential sums on the torus gm n extend via the usual toric decomposition of an to exponential sums on affine n space and finally proceed via a standard character argument 4 to exponential sums on an affine variety defined over fq while this is the natural order of the work what we do in fact in the first part of this article is to combine the first two steps and deal with exponential sums on varieties v of the form v gm r x as r s n let f e fq xl xn xl xr be an arbitrary regular function on v then f is a sum of monomials and as such has a well defined newton polyhedron a ff at infinity this is the convex closure in rn of the lattice points which occur as exponents of the terms of f together with the origin we have indicated in our previous work 1 2 the description of some of the invariants of the associated l function in terms of properties of this polyhedron for example in 1 we showed how bounds for the degree and total degree of the l function associated with a general exponential sum on v can be expressed in terms of the volumes of a f and the intersections of a f and the various coordinate spaces in the present article assuming f is nondegenerate and commode with respect to af f we show these estimates are sharp our methods are p adic and are based on the work of dwork 11 12 our main accomplishment from which our other results follow is the extension of dwork s cohomology theory from smooth projective hypersurfaces in characteristic p to a general class of exponential sums given f regular on v we construct a complex of p adic banach spaces on which frobenius acts the alternating product of characteristic polynomials of frobenius describes the associated l function in fact when f is nondegenerate and commode with respect to a f the complex is acyclic in dimensions other than 0 and the characteristic

hodge genera of algebraic varieties ii we study the behavior of hodge genera under algebraic maps we prove thatthemotivic c y genussatisfiesthe stratifiedmultiplicativeproperty whichshows how to compute the invariant of the source of a morphism from its values on varieties arising from the singularities of the map by considering morphisms to a curve we obtain a hodge theoretic version of the riemann hurwitz formula we also study the monodromy contributions to the y genus of a family of compact complex manifolds and prove an atiyah meyer type formula in the algebraic and analytic contexts this formula measures the deviation from multiplicativity of the y genus and expresses the correction terms as higher genera associated to the period map these higher gen era are hodge theoretic extensions of novikov higher signatures to analytic and alge braic settings characteristic class formulae of atiyah meyer type are also obtained by making use of saito s theory of mixed hodge modules

convex polytopes and quasilattices from the symplectic viewpoint we construct for each convex polytope possibly nonrational and nonsimple a family of compact spaces that are stratified by quasifolds i e each of these spaces is a collection of quasifolds glued together in an suitable way a quasifold is a space locally modelled on mathbb r k modulo the action of a discrete possibly infinite group the way strata are glued to each other also involves the action of an infinite discrete group each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back these spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting

exponential sums on ⁿ ii we prove a vanishing theorem for the p adic cohomology of exponential sums on a n in particular we obtain new classes of exponential sums on an that have a single nonvanishing p adic cohomology group the dimension of this cohomology group equals a sum of milnor numbers

pilot aided ofdm channel estimation in the presence of the guard band in this letter pilot design and channel estimation are discussed for orthogonal frequency division multiplexing ofdm systems with guard subcarriers first we investigate the effects of guard band on channel estimation errors from this we propose pilot placement having a maximum distance between adjacent pilots except for the guard band and show that it achieves minimum channel estimation errors among partially equispaced pilots using equivalence of the toeplitz and circulant matrices also an efficient channel estimator is developed by introducing an extended channel and its finite impulse response fir approximation to overcome high numerical complexity caused by the presence of guard subcarriers and the use of a large number of subcarriers simulation results are presented for ofdm and orthogonal frequency division multiple access ofdma systems consistent with ieee 802 16a standards

local h polynomials invariants of subdivisions and mixed ehrhart theory abstract there are natural polynomial invariants of polytopes and lattice polytopes coming from enumerative combinatorics and ehrhart theory namely the h and h polynomials respectively in this paper we study their generalization to subdivisions and lattice subdivisions of polytopes by abstracting constructions in mixed hodge theory we introduce multivariable polynomials which specialize to the h h polynomials these polynomials the mixed h polynomial and the refined limit mixed h polynomial have rich symmetry non negativity and unimodality properties which both refine known properties of the classical polynomials and reveal new structure for example we prove a lower bound theorem for a related invariant called the local h polynomial we introduce our polynomials by developing a very general formalism for studying subdivisions of eulerian posets that extends the work of stanley brenti and athanasiadis on local h vectors in particular we prove a conjecture of nill and schepers and answer a question of athanasiadis

the chow groups and the motive of the hilbert scheme of points on a surface abstract we compute the chow motive and the chow groups with rational coefficients of the hilbert scheme of points on a smooth algebraic surface

relative hard lefschetz theorem for fans abstract we prove the relative hard lefschetz theorem and the relative hodge riemann bilinear relations for combinatorial intersection cohomology sheaves on fans

evaluation of 4d flow mri based non invasive pressure assessment in aortic coarctations abstract severity of aortic coarctation coa is currently assessed by estimating trans coarctation pressure drops through cardiac catheterization or echocardiography in principle more detailed information could be obtained non invasively based on space and time resolved magnetic resonance imaging 4d flow data yet the limitations of this imaging technique require testing the accuracy of 4d flow derived hemodynamic quantities against other methodologies with the objective of assessing the feasibility and accuracy of this non invasive method to support the clinical diagnosis of coa we developed an algorithm 4df feppe to obtain relative pressure distributions from 4d flow data by solving the poisson pressure equation 4df feppe was tested against results from a patient specific fluid structure interaction fsi simulation whose patient specific boundary conditions were prescribed based on 4d flow data since numerical simulations provide noise free pressure fields on fine spatial and temporal scales our analysis allowed to assess the uncertainties related to 4d flow noise and limited resolution 4df feppe and fsi results were compared on a series of cross sections along the aorta bland altman analysis revealed very good agreement between the two methodologies in terms of instantaneous data at peak systole end diastole and time averaged values biases means of differences were 0 4 mmhg 1 1 mmhg and 0 6 mmhg respectively limits of agreement 2 sd were 0 978 mmhg 1 06 mmhg and 1 97 mmhg respectively peak to peak and maximum trans coarctation pressure drops obtained with 4df feppe differed from fsi results by 0 75 mmhg and 1 34 mmhg respectively the present study considers important validation aspects of non invasive pressure difference estimation based on 4d flow mri showing the potential of this technology to be more broadly applied to the clinical practice

mellin transformation propagation and abelian duality spaces abstract for arbitrary field coefficients k we show that k perverse sheaves on a complex affine torus satisfy the so called propagation package i e the generic vanishing property and the signed euler characteristic property hold and the corresponding cohomology jump loci satisfy the propagation property and codimension lower bound the main ingredient used in the proof is gabber loeser s mellin transformation functor for k constructible complexes on a complex affine torus and the fact that it behaves well with respect to perverse sheaves as a concrete topological application of our sheaf theoretic results we study homological duality properties of complex algebraic varieties via abelian duality spaces we provide new obstructions on abelian duality spaces by showing that their cohomology jump loci satisfy a propagation package this is then used to prove that complex abelian varieties are the only complex projective manifolds which are abelian duality spaces we also construct new examples of abelian duality spaces for example we show that if a smooth quasi projective variety x satisfies a certain hodge theoretic condition and it admits a proper semi small map e g a closed embedding or a finite map to a complex affine torus then x is an abelian duality space

mirror duality and string theoretic hodge numbers we prove in full generality the mirror duality conjecture for string theoretic hodge numbers of calabi yau complete intersections in gorenstein toric fano varieties the proof is based on properties of intersection cohomology

the circle method and bounds for l functions ii subconvexity for twists of gl 3 l functions let pi be a rm sl 3 bbb z hecke maass cusp form let chi chi 1 chi 2 be a dirichlet character with chi i primitive modulo m i suppose m 1 m 2 are primes such that sqrt m 2 m 4 delta m 1 m 2m 3 delta where m m 1m 2 and 0 delta 1 28 in this paper we will prove the following subconvex bound l left 1 over 2 pi otimes chi right ll pi varepsilon m 3 over 4 delta varepsilon

the hodge theory of soergel bimodules we prove soergel s conjecture on the characters of indecomposable soergel bimodules we deduce that kazhdan lusztig polynomials have positive coecients for arbitrary coxeter systems using results of soergel one may deduce an algebraic proof of the kazhdan lusztig conjecture

intersection homology ii in 19 20 we introduced topological invariants ih x called intersection homology groups for the study of singular spaces x these groups depend on the choice of a perversity p a perversity is a function from 2 3 to the non negative integers such that both c and c 2 c are positive and increasing functions of c 2 1 the group ihr is defined for spaces x called pseudomanifolds a pseudomanifold of dimension n is a space that admits a stratification x x n x n z x n 3 x 1 x 0

geometric langlands duality and representations of algebraic groups over commutative rings as such it can be viewed as a first step in the geometric langlands program the connected complex reductive groups have a combinatorial classification by their root data in the root datum the roots and the co roots appear in a symmetric manner and so the connected reductive algebraic groups come in pairs if g is a reductive group we write g for its companion and call it the dual group g the notion of the dual group itself does not appear in satake s paper but was introduced by langlands together with its various elaborations in li l2 and is a cornerstone of the langlands program it also appeared later in physics mo gno in this paper we discuss the basic relationship between g and g we begin with a reductive g and consider the affine grassmannian qx the grassmannian for the loop group of g for technical reasons we work with formal algebraic loops the affine grassmannian is an infinite dimen sional complex space we consider a certain category of sheaves the spherical perverse sheaves on r these sheaves can be multiplied using a convolution product and this leads to a rather explicit construction of a hopf algebra by what has come to be known as tannakian formalism the resulting hopf algebra turns out to be the ring of functions on g in this interpretation the spherical perverse sheaves on the affine grassman nian correspond to finite dimensional complex representations of g thus instead of defining g in terms of the classification of reductive groups we pro vide a canonical construction of g starting from g we can carry out our construction over the integers the spherical perverse sheaves are then those with integral coefficients but the grassmannian remains a complex algebraic object

pilot design for mimo ofdm systems with virtual carriers we consider the problem of pilot design for channel estimation in multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems in the presence of virtual carriers the design criterion is the average mean square error mse of the least square ls estimates of the channel frequency response over the data carriers to maximize bandwidth efficiency the number of pilots is set to its minimum which is equal to the number of unknown channel coefficients both the phase shift orthogonal and disjoint pilot schemes are investigated for a given pilot placement a closed form expression for the pilot power distribution for the disjoint scheme is provided it is found that the optimal power distribution allocates less power to the pilots that are close to the virtual carriers pilot placement is obtained using an exhaustive search the latter is too complex in systems with large number of subcarriers a suboptimum pilot placement design for the disjoint pilot scheme is presented it is shown that unlike fully loaded systems where the two pilot design schemes have similar performance in the presence of virtual carriers the optimal disjoint scheme not only has lower complexity but also yields more accurate channel estimation and bit error rate performance

l adic gkz hypergeometric sheaves and exponential sums abstract to a torus action on a complex vector space gelfand kapranov and zelevinsky introduce a system of differential equations called the gkz hypergeometric system its solutions are gkz hypergeometric functions we study the l adic counterpart of the gkz hypergeometric system which we call the l adic gkz hypergeometric sheaf it is an object in the derived category of l adic sheaves on the affine space over a finite field traces of frobenius on stalks of this object at rational points of the affine space define the hypergeometric functions over the finite field introduced by gelfand and graev we prove that the l adic gkz hypergeometric sheaf is perverse calculate its rank and prove that it is irreducible under the non resonance condition we also study the weight filtration of the gkz hypergeometric sheaf determine its lisse locus and apply our result to the study of weights of twisted exponential sums

frobenius semisimplicity for convolution morphisms this article concerns properties of mixed ell adic complexes on varieties over finite fields related to the action of the frobenius automorphism we establish a fiberwise criterion for the semisimplicity and frobenius semisimplicity of the direct image complex under a proper morphism of varieties over a finite field we conjecture that the direct image of the intersection complex on the domain is always semisimple and frobenius semisimple this conjecture would imply that a strong form of the decomposition theorem of beilinson bernstein deligne gabber is valid over finite fields we prove our conjecture for generalized convolution morphisms associated with partial affine flag varieties for split connected reductive groups over finite fields as a crucial tool we develop a new schematic theory of big cells for loop groups with suitable reformulations the main results are valid over any algebraically closed ground field

a geometric degree formula for a discriminants and euler obstructions of toric varieties abstract we give explicit formulas for the dimensions and the degrees of a discriminant varieties introduced by gelfand kapranov and zelevinsky our formulas can be applied also to the case where the a discriminant varieties are higher codimensional and their degrees are described by the geometry of the configurations a moreover combinatorial formulas for the euler obstructions of general not necessarily normal toric varieties will be also given

the intersection cohomology of the satake compactification of mathcal a _g for g le 4 we completely determine the intersection cohomology of the satake compactifications mathcal a 2 mathrm sat mathcal a 3 mathrm sat and mathcal a 4 mathrm sat except for ih 10 mathcal a 4 mathrm sat we also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the satake compactification in these genera as a byproduct we obtain in addition several results about the intersection cohomology of the link bundles involved

parabolic refined invariants and macdonald polynomials a string theoretic derivation is given for the conjecture of hausel letellier and rodriguez villegas on the cohomology of character varieties with marked points their formula is identified with a refined bps expansion in the stable pair theory of a local root stack generalizing previous work of the first two authors in collaboration with pan haiman s geometric construction for macdonald polynomials is shown to emerge naturally in this context via geometric engineering in particular this yields a new conjectural relation between macdonald polynomials and refined local orbifold curve counting invariants the string theoretic approach also leads to a new spectral cover construction for parabolic higgs bundles in terms of holomorphic symplectic orbifolds

intersection homology and torus actions in the bialynicki birula decomposition of x see 15 6 10 13 the same formula holds for appropriate integers my when c is replaced by a torus t c r in 9 it is shown that the formula 0 1 is valid even when x is singular provided that the bialynicki birula decomposition is good the aim of this paper is to generalize 0 1 to the case when x is singular in a different way which involves replacing ordinary homology by intersection homology with respect to the middle perversity however only rational coefficients are considered when x is nonsingular its intersection homology and ordinary homology coincide but when x is singular its intersection homology behaves better in many respects than its ordinary cohomology it is shown that when x is singular just as when x is nonsingular the rational intersection homology of x is determined by the action of t on an arbitrarily small neighborhood of the fixed point set xt as might be expected the formula 0 1 does not carry over directly when intersection homology replaces ordinary homology the terms hi 2m f z appearing in the right hand side are replaced by hypercohomology groups of certain complexes of sheaves over the f which depend upon how the f meet the singularities of x see they y orem 2 3 1 of this paper contains a review of a proof of 0 1 for rational coefficients which uses equivariant morse theory in 2 it is shown how this proof can be extended to apply to singular varieties when intersection homology is used the

cohomology of line bundles applications massless modes of both heterotic and type ii string compactifications on compact manifolds are determined by vector bundle valued cohomology classes various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented for the heterotic string the prime examples are so called monad constructions on calabi yau manifolds in the context of type ii orientifolds one often needs to compute cohomology for line bundles on finite group action coset spaces necessitating us to generalize our algorithm to this case moreover we exemplify that the different terms in batyrev s formula and its generalizations can be given a one to one cohomological interpretation furthermore we derive a combinatorial closed form expression for two hodge numbers of a codimension two calabi yau fourfold

perverse sheaves on real loop grassmannians the aim of this paper is to identify a certain tensor category of perverse sheaves on the loop grassmannian gr of a real form g of a connected reductive complex algebraic group g with the category of finite dimensional representations of a connected reductive complex algebraic subgroup check h of the dual group check g the root system of check h is closely related to the restricted root system of g the fact that check h is reductive implies that an interesting family of real algebraic maps satisfies the conclusion of the decomposition theorem of beilinson bernstein deligne

hodge genera of algebraic varieties i the aim of this paper is to study the behavior of hodge theoretic intersection homology genera and their associated characteristic classes under proper morphisms of complex algebraic varieties we obtain formulae that relate parametrized families of global invariants of a complex algebraic variety x to such invariants of singularities of proper algebraic maps defined on x such formulae severely constrain both topologically and analytically the singularities of complex maps even between smooth varieties similar results were announced by the first and third author in 13 32 2007 wiley periodicals inc

the kazhdan lusztig polynomial of a matroid abstract we associate to every matroid m a polynomial with integer coefficients which we call the kazhdan lusztig polynomial of m in analogy with kazhdan lusztig polynomials in representation theory we conjecture that the coefficients are always non negative and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology poincare polynomials we also introduce a q deformation of the mobius algebra of m and use our polynomials to define a special basis for this deformation analogous to the canonical basis of the hecke algebra we conjecture that the structure coefficients for multiplication in this special basis are non negative and we verify this conjecture in numerous examples

the hypertoric intersection cohomology ring we present a functorial computation of the equivariant intersection cohomology of a hypertoric variety and endow it with a natural ring structure when the hyperplane arrangement associated with the hypertoric variety is unimodular we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category the computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice stratified space to sheaves on a poset

euler characteristics of algebraic varieties this note studies the behavior of euler characteristics and of intersection homology euler characteristics under proper morphisms of algebraic respectively analytic varieties the methods also yield for algebraic respectively analytic varieties formulae comparing these two kinds of euler characteristics the main results are direct consequences of the calculus of constructible functions and grothendieck groups of constructible sheaves similar formulae for hodgetheoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in 5 14 c 2007 wiley periodicals inc

zeta functions and oscillatory integrals for meromorphic functions abstract in the 70 s igusa developed a uniform theory for local zeta functions and oscillatory integrals attached to polynomials with coefficients in a local field of characteristic zero in the present article this theory is extended to the case of rational functions or more generally meromorphic functions f g with coefficients in a local field of characteristic zero this generalization is far from being straightforward due to the fact that several new geometric phenomena appear also the oscillatory integrals have two different asymptotic expansions the usual one when the norm of the parameter tends to infinity and another one when the norm of the parameter tends to zero the first asymptotic expansion is controlled by the poles with negative real parts of all the twisted local zeta functions associated to the meromorphic functions f g c for certain special values c the second expansion is controlled by the poles with positive real parts of all the twisted local zeta functions associated to f g

purity of exponential sums on n ii we give a purity result for exponential sums of the type x2kn f x where k is a flnite fleld of characteristic p k c is a non trivial additive character and f 2 k x1 xn is a polynomial whose highest degree homogeneous form splits as a product of factors deflning a divisor with normal crossings in p ni1

topology of hitchin systems and hodge theory of character varieties the case a1 for g gl2 pgl2 sl2 we prove that the perverse ltration associated with the hitchin map on the rational cohomology of the moduli space of twisted g higgs bundles on a compact riemann surface c agrees with the weight ltration on the rational cohomology of the twisted g character variety of c when the cohomologies are identied via non abelian hodge theory the proof is accomplished by means of a study of the topology of the hitchin map over the locus of integral spectral curves

the monodromy theorem for compact kahler manifolds and smooth quasi projective varieties given any connected topological space x assume that there exists an epimorphism phi pi 1 x rightarrow mathbb z the deck transformation group mathbb z acts on the associated infinite cyclic cover x phi of x hence on the homology group h i x phi mathbb c this action induces a linear automorphism on the torsion part of the homology group as a module over the laurent ring mathbb c t t 1 which is a finite dimensional mathbb c vector space we study the sizes of the jordan blocks of this linear automorphism when x is a compact kahler manifold we show that all the jordan blocks are of size one when x is a smooth complex quasi projective variety we give an upper bound on the sizes of the jordan blocks which is an analogue of the monodromy theorem for the local milnor fibration

character sums associated to finite coxeter groups we prove a character sum identity for coxeter arrangements which is a finite field analogue of macdonald s conjecture proved by opdam

hard lefschetz theorem for nonrational polytopes the hard lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope one can construct the intersection cohomology combinatorially from the polytope hence it is well defined even for nonrational polytopes when there is no variety associated to it we prove the hard lefschetz theorem for the intersection cohomology of a general polytope

monodromy of the sl n and gl n hitchin fibrations we compute the monodromy of the hitchin fibration for the moduli space of l twisted sl n mathbb c and gl n mathbb c higgs bundles for any n on a compact riemann surface of genus g 1 we require the line bundle l to either be the canonical bundle or satisfy deg l 2g 2 the monodromy group is generated by picard lefschetz transformations associated to vanishing cycles of singular spectral curves we construct such vanishing cycles explicitly and use this to show that the sl n mathbb c monodromy group is a skew symmetric vanishing lattice in the sense of janssen using the classification of vanishing lattices over mathbb z we completely determine the structure of the monodromy groups of the sl n mathbb c and gl n mathbb c hitchin fibrations as an application we determine the image of the restriction map from the cohomology of the moduli space of higgs bundles to the cohomology of a non singular fibre of the hitchin fibration