inseparable local uniformization abstract it is known since the works of zariski in the early 40s that desingularization of varieties along valuations called local uniformization of valuations can be considered as the local part of the desingularization problem it is still an open problem if local uniformization exists in positive characteristic and dimension larger than three in this paper we prove that zariski local uniformization of algebraic varieties is always possible after a purely inseparable extension of the field of rational functions and therefore any valuation can be uniformized by a purely inseparable alteration

the schwarz lemma at the boundary of the symmetrized bidisc abstract the symmetrized bidisc g 2 is defined by g 2 z 1 z 2 z 1 z 2 c 2 z 1 1 z 2 1 z 1 z 2 c it is a bounded inhomogeneous pseudoconvex domain without c 1 boundary and especially the symmetrized bidisc hasn t any strongly pseudoconvex boundary point and the boundary behavior of both caratheodory and kobayashi metrics over the symmetrized bidisc is hard to describe precisely in this paper we study the boundary schwarz lemma for holomorphic self mappings of the symmetrized bidisc g 2 and our boundary schwarz lemma in the paper differs greatly from the earlier related results

fixed points koebe uniformization and circle packings a domain in the riemann sphere hat mathbb c is called a circle domain if every connected component of its boundary is either a circle or a point in 1908 p koebe ko1 posed the following conjecture known as koebe s kreisnormierungsproblem any plane domain is conformally homeomorphic to a circle domain in hat mathbb c when the domain is simply connected this is the content of the riemann mapping theorem

an iterative method for linear discrete ill posed problems with box constraints many questions in science and engineering give rise to linear discrete ill posed problems often it is desirable that the computed approximate solution satisfies certain constraints e g that some or all elements of the computed solution be nonnegative this paper describes an iterative method of active set type for the solution of large scale problems of this kind the method employs conjugate gradient iteration with a stopping criterion based on the discrepancy principle and allows updates of the active set by more than one index at a time

rigidity of holomorphic mappings and a new schwarz lemma at the boundary a rigidity theorem for holomorphic mappings in the nature of the uniqueness statement of the classical one variable schwarz lemma is proved at the boundary of a strongly pseudoconvex domain the result reduces to an interesting and apparently new result even in one complex dimension the theorem has a variety of geometric and analytic interpretations department of mathematics university of michigan ann arbor michigan 48109 department of mathematics box 1146 washington university in st louis st louis missouri 63130 this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 04 utc all use subject to http about jstor org terms

schwarz lemma at the boundary of strongly pseudoconvex domain in mathbb c n in this paper we establish a new type of the classical boundary schwarz lemma for holomorphic self mappings of strongly pseudoconvex domain in mathbb c n

hopf algebras for matroids over hyperfields abstract recently m baker and n bowler introduced the notion of matroids over hyperfields as a unifying theory of various generalizations of matroids in this paper we generalize the notion of minors and direct sums from ordinary matroids to matroids over hyperfields using this we generalize the classical construction of matroid minor hopf algebras to the case of matroids over hyperfields

discontinuous parameter estimates with least squares estimators we discuss weighted least squares estimates of ill conditioned linear inverse problems where weights are chosen to be inverse error covariance matrices least squares estimators are the maximum likelihood estimate for normally distributed data and parameters but here we do not assume particular probability distributions weights for the estimator are found by ensuring its minimum follows a g 2 distribution previous work with this approach has shown that it is competitive with regularization methods such as the l curve and generalized cross validation gcv 20 in this work we extend the method to find diagonal weighting matrices rather than a scalar regularization parameter diagonal weighting matrices are advantageous because they give piecewise smooth least squares estimates and hence are a mechanism through which least squares can be used to estimate discontinuous parameters this is explained by viewing least squares estimation as a constrained optimization problem results with diagonal weighting matrices are given for a benchmark discontinuous inverse problem from 13 in addition the method is used to estimate soil moisture from data collected in the dry creek watershed near boise idaho parameter estimates are found that combine two different types of measurements and weighting matrices are found that incorporate uncertainty due to spatial variation so that the parameters can be used over larger scales than those that were measured

extremal bundles on calabi yau threefolds we study constructions of stable holomorphic vector bundles on calabi yau threefolds especially those with exact anomaly cancellation which we call extremal by going through the known databases we find that such examples are rare in general and can be ruled out for the spectral cover construction for all elliptic threefolds we then introduce a general hartshorne serre construction and use it to find extremal bundles of general ranks and study their stability as well as computing their chern numbers based on both existing and our new constructions we revisit the dry conjecture for the existence of stable sheaves on calabi threefolds and provide theoretical and numerical evidence for its correctness our construction can be easily generalized to bundles with no extremal conditions imposed

lissite du schema de hilbert en bas degre abstract we check that the hilbert scheme h d g of smooth and connected curves of degree d and genus g in projective three dimensional space over c is smooth provided that d 11 the proof uses essentially our good knowledge of curves lying on cubic surfaces and the possibility to endow a curve having a special normal bundle with a double structure of high arithmetic genus then we give some partial results in the case of degree 12 namely we obtain that h 12 g is smooth for g h 12 g is smooth in codimension 1 this shows that 12 15 is the lexicographically first pair d g such that h d g is singular in codimension 1

on the moduli space of diffeomorphic algebraic surfaces in this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four manifold can be arbitrarily large the examples that we consider in this paper are locally simple abelian covers of rational surfaces the proof involves the algebraic description of rational blowdowns classical brill noether theory and deformation theory of normal flat abelian covers

rigidity of proper holomorphic self mappings of the pentablock abstract the pentablock is a hartogs domain in c 3 over the symmetrized bidisc in c 2 the domain is a bounded inhomogeneous pseudoconvex domain which does not have a c 1 boundary recently agler lykova young constructed a special subgroup of the group of holomorphic automorphisms of the pentablock and kosinski fully described the group of holomorphic automorphisms of the pentablock the aim of the present study is to prove that any proper holomorphic self mapping of the pentablock must be an automorphism

semi local scaling exponent estimation with box penalty constraints and total variation regularization we here establish and exploit the result that 2d isotropic self similar fields beget quasi decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal this leads to the development of a semi local scaling exponent estimation framework with optimally modified weights furthermore recent interest in penalty methods for least square problems and generalized lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least square estimator framework numerical results on fractional brownian fields with global and piecewise constant semi local hurst parameters illustrate the benefits of the new estimators

schwarz lemma and rigidity theorem at the boundary for holomorphic mappings on the unit polydisk in cn abstract this article is devoted to a deep study of holomorphic self mappings of the unit polydisk via not only establishing a new type of the classical schwarz lemma at the boundary but also giving the boundary version of the rigidity theorem

murphy s law in algebraic geometry badly behaved deformation spaces we consider the question how bad can the deformation space of an object be the answer seems to be unless there is some a priori reason otherwise the deformation space may be as bad as possible we show this for a number of important moduli spaces more precisely every singularity of finite type over up to smooth parameters appears on the hilbert scheme of curves in projective space and the moduli spaces of smooth projective general type surfaces or higher dimensional varieties plane curves with nodes and cusps stable sheaves isolated threefold singularities and more the objects themselves are not pathological and are in fact as nice as can be the curves are smooth the surfaces are automorphism free and have very ample canonical bundle the stable sheaves are torsion free of rank 1 the singularities are normal and cohen macaulay etc this justifies mumford s philosophy that even moduli spaces of well behaved objects should be arbitrarily bad unless there is an a priori reason otherwise thus one can construct a smooth curve in projective space whose deformation space has any given number of components each with any given singularity type with any given non reduced behavior similarly one can give a surface over mathbb f p that lifts to p 7 but not p 8 of course the results hold in the holomorphic category as well it is usually difficult to compute deformation spaces directly from obstruction theories we circumvent this by relating them to more tractable deformation spaces via smooth morphisms the essential starting point is mnev s universality theorem

hypersurfaces with defect abstract a projective hypersurface x p n has defect if h i x h i p n for some i n 2 n 2 in a suitable cohomology theory this occurs for example when x p 4 is not q factorial we show that hypersurfaces with defect tend to be very singular in characteristic 0 we present a lower bound on the tjurina number where x is allowed to have arbitrary isolated singularities for x with mild singularities we prove a similar result in positive characteristic as an application we obtain an estimate on the asymptotic density of hypersurfaces without defect over a finite field

the two by two spectral nevanlinna pick problem we give a criterion for the existence of an analytic 2 x 2 matrix valued function on the disc satisfying a finite set of interpolation conditions and having spectral radius bounded by 1 we also give a realization theorem for analytic functions from the disc to the symmetrised bidisc

newton s method for large bound constrained optimization problems we analyze a trust region version of newton s method for bound constrained problems our approach relies on the geometry of the feasible set not on the particular representation in terms of constraints the convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints we also show that the convergence theory leads to an efficient implementation for large bound constrained problems

identity principles for commuting holomorphic self maps of the unit disc abstract let f g be two commuting holomorphic self maps of the unit disc if f and g agree at the common wolff point up to a certain order of derivatives no more than 3 if the wolff point is on the unit circle then f g

quiver grassmannians and auslander varieties for wild algebras let k be an algebraically closed field and a finite dimensional k algebra given a module m the set ge m of all submodules of m with dimension vector e is called a quiver grassmannian if d y are modules then we consider hom d y as a d module where d end d op and the auslander varieties for are the quiver grassmannians of the form gehom d y quiver grassmannians thus also auslander varieties are projective varieties and it is known that every projective variety occurs in this way there is a tendency to relate this fact to the wildness of quiver representations and the aim of this note is to clarify these thoughts we show that for an algebra which is controlled wild any projective variety can be realized as an auslander variety but not necessarily as a quiver grassmannian

the singularities of the principal component of the hilbert scheme of points abstract haiman proved the remarkable result that the isospectral hilbert scheme of points in the plane is normal cohen macaulay and gorenstein this implies the n conjecture and the positivity conjecture for the kostka macdonald coefficients in addition he conjectured that the isospectral hilbert scheme over the principal component of hilb n c d is cohen macaulay for any d n 1 we provide a counterexample to the conjecture

a trust region approach to the regularization of large scale discrete forms of ill posed problems we consider large scale least squares problems where the coefficient matrix comes from the discretization of an operator in an ill posed problem and the right hand side contains noise special techniques known as regularization methods are needed to treat these problems in order to control the effect of the noise on the solution we pose the regularization problem as a quadratically constrained least squares problem this formulation is equivalent to tikhonov regularization and we note that it is also a special case of the trust region subproblem from optimization we analyze the trust region subproblem in the regularization case and we consider the nontrivial extensions of a recently developed method for general large scale subproblems that will allow us to handle this case the method relies on matrix vector products only has low and fixed storage requirements and can handle the singularities arising in ill posed problems we present numerical results on test problems on an inverse interpolation problem with field data and on a model seismic inversion problem with field data

schwarz s lemma for circle packings burt rodin department of mathematics university of california la jolla ca 92093 usa 1 introduction conformal mappings can be approximated by circle packing isomorphisms this is proved in 10 roughly speaking see sect 5 for a more detailed description a bounded region f2 is almost filled by e circles 7 from the regular hexagonal e circle packing of the plane denote this approximate circle pack ing of q by q by results of andreev and thurston there is a combinatorially isomorphic circle packing d of the unit disk d denote this isomorphism suitably normalized by 7 7 f2 d let f be the piecewise linear quasicon formal mapping determined by the associated triangulations as e 0 f con verges uniformly on compacta to the riemann mapping function f f2 d let

the ubiquity of smooth hilbert schemes we investigate the geography of hilbert schemes parametrizing closed subschemes of projective space with specified hilbert polynomials we classify hilbert schemes with unique borel fixed points via combinatorial expressions for their hilbert polynomials these expressions naturally lead to an arrangement of nonempty hilbert schemes as the vertices of an infinite full binary tree here we discover regularities in the geometry of hilbert schemes specifically under natural probability distributions on the tree we prove that hilbert schemes are irreducible and nonsingular with probability greater than 0 5

least squares problems with inequality constraints as quadratic constraints abstract linear least squares problems with box constraints are commonly solved to find model parameters within bounds based on physical considerations common algorithms include bounded variable least squares bvls and the matlab function lsqlin here the goal is to find solutions to ill posed inverse problems that lie within box constraints to do this we formulate the box constraints as quadratic constraints and solve the corresponding unconstrained regularized least squares problem using box constraints as quadratic constraints is an efficient approach because the optimization problem has a closed form solution the effectiveness of the proposed algorithm is investigated through solving three benchmark problems and one from a hydrological application results are compared with solutions found by lsqlin and the quadratically constrained formulation is solved using the l curve maximum a posteriori estimation map and the 2 regularization method the 2 regularization method with quadratic constraints is the most effective method for solving least squares problems with box constraints

pathologies on the hilbert scheme of points we prove that the hilbert scheme of points on a higher dimensional affine space is non reduced and has components lying entirely in characteristic p for all primes p in fact we show that vakil s murphy s law holds up to retraction for this scheme our main tool is a generalized version of the bialynicki birula decomposition

local structure of abelian covers abstract we study normal finite abelian covers of smooth varieties in particular we establish combinatorial conditions so that a normal finite abelian cover of a smooth variety is gorenstein or locally complete intersection

extremal holomorphic maps and the symmetrized bidisc we analyze the 3 extremal holomorphic maps from the unit disc mathbb d to the symmetrized bidisc mathcal g mathop limits mathrm def z w zw z w in mathbb d with a view to the complex geometry and function theory of mathcal g these are the maps whose restriction to any triple of distinct points in mathbb d yields interpolation data that are only just solvable we find a large class of such maps they are rational of degree at most 4 it is shown that there are two qualitatively different classes of rational mathcal g inner functions of degree at most 4 to be called aligned and caddywhompus functions the distinction relates to the cyclic ordering of certain associated points on the unit circle the aligned ones are 3 extremal we describe a method for the construction of aligned rational mathcal g inner functions with the aid of this method we reduce the solution of a 3 point interpolation problem for aligned holomorphic maps from mathbb d to mathcal g to a collection of classical nevanlinna pick problems with mixed interior and boundary interpolation nodes proofs depend on a form of duality for mathcal g

on rigid compact complex surfaces and manifolds abstract this article investigates the subject of rigid compact complex manifolds first of all we investigate the different notions of rigidity local rigidity global rigidity infinitesimal rigidity etale rigidity and strong rigidity and the relations among them only for curves these notions coincide and the only rigid curve is the projective line for surfaces we prove that a rigid surface which is not minimal of general type is either a del pezzo surface of degree 5 or an inoue surface we give examples of rigid manifolds of dimension n 3 and kodaira dimensions 0 and 2 k n our main theorem is that the hirzebruch kummer coverings of exponent n 4 branched on a complete quadrangle are infinitesimally rigid moreover we pose a number of questions

smooth and irreducible multigraded hilbert schemes abstract the multigraded hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed hilbert function we prove that any multigraded hilbert scheme is smooth and irreducible when the polynomial ring is z x y which establishes a conjecture of haiman and sturmfels