68 citations · 258 across the 40 of their papers we have counts for
30 papers · 1 filter
Hypergeometric systems from groups with torsion
Thomas Reichelt, Christian Sevenheck, Uli Walther
We consider -hypergeometric (or GKZ-)systems in the case where the grading (character) group is an arbitrary finitely generated Abelian group. Emulating the approach taken for c…
Tautological systems, homogeneous spaces and the holonomic rank problem
Paul Görlach, Thomas Reichelt, Christian Sevenheck +2
Many hypergeometric differential systems that arise from a geometric setting can be endowed with the structure of mixed Hodge modules. We generalize this fundamental result to the…
Topological calculation of local cohomological dimension
Thomas Reichelt, Morihiko Saito, Uli Walther
We show that the sum of the local cohomological dimension and the rectified -homological depth of a closed analytic subspace of a complex manifold coincide with the dime…
On Lyubeznik type invariants
Thomas Reichelt, Uli Walther, Wenliang Zhang
We discuss for an affine variety embedded in affine space two sets of integers attached to via local and de Rham cohomology spectral sequences. We give topol…
Configuration polynomials under contact equivalence
Graham Denham, Delphine Pol, Mathias Schulze +1
Configuration polynomials generalize the classical Kirchhoff polynomial defined by a graph. Their study sheds light on certain polynomials appearing in Feynman integrands. Contact…
Graph hypersurfaces with torus action and a conjecture of Aluffi
Graham Denham, Delphine Pol, Mathias Schulze +1
Generalizing the star graphs of Müller-Stach and Westrich, we describe a class of graphs whose associated graph hypersurface is equipped with a non-trivial torus action. For such g…
Algebraic aspects of hypergeometric differential equations
Thomas Reichelt, Mathias Schulze, Christian Sevenheck +1
We review some classical and modern aspects of hypergeometric differential equations, including -hypergeometric systems of Gel'fand, Graev, Kapranov and Zelevinsky. Some recent…
Matroid connectivity and singularities of configuration hypersurfaces
Graham Denham, Mathias Schulze, Uli Walther
Consider a linear realization of a matroid over a field. One associates with it a configuration polynomial and a symmetric bilinear form with linear homogeneous coefficients. The c…
Weight filtrations on GKZ-systems
Thomas Reichelt, Uli Walther
If $β\in\CC^d$ is integral but not a strongly resonant parameter for the homogeneous matrix $A\in\ZZ^{d\times n}$ with $\ZZ A=\ZZ^d$, then the associated GKZ-system carries a natur…
On normalized Horn systems
Christine Berkesch, Laura Felicia Matusevich, Uli Walther
We characterize the (regular) holonomicity of Horn systems of differential equations under a hypothesis that captures the most widely studied classical hypergeometric systems.
On categories of equivariant D-modules
András C. Lőrincz, Uli Walther
Let be a variety with an action by an algebraic group . In this paper we discuss various properties of -equivariant -modules on , such as the decompositions of thei…
Dependence of Lyubeznik numbers of cones of projective schemes on projective embeddings
Thomas Reichelt, Morihiko Saito, Uli Walther
We construct complex projective schemes with Lyubeznik numbers of their cones depending on the choices of projective embeddings. This answers a question of G. Lyubeznik in the char…
Gauss-Manin systems of families of Laurent polynomials and A-hypergeometric systems
Thomas Reichelt, Uli Walther
In this note we study families of Gauss-Manin systems arising from Laurent polynomials with parametric coefficients under projection to the parameter space. For suitable matrices o…
Bernstein-Sato polynomials for maximal minors and sub-maximal Pfaffians
András C. Lőrincz, Claudiu Raicu, Uli Walther +1
We determine the Bernstein-Sato polynomials for the ideal of maximal minors of a generic m x n matrix, as well as for that of sub-maximal Pfaffians of a generic skew-symmetric matr…
On the -functions of hypergeometric systems
Thomas Reichelt, Christian Sevenheck, Uli Walther
For any integer matrix and parameter $β\in\CC^d$ let be the associated -hypergeometric (or GKZ) system in the variables . We describ…
Survey on the -module
Anton Leykin, Uli Walther
In this survey we discuss various aspects of the singularity invariants with differential origin derived from the -module generated by .
The Jacobian module, the Milnor fiber, and the -module generated by
Uli Walther
For a germ on a complex manifold , we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness criterion. We use t…
Torus equivariant D-modules and hypergeometric systems
Christine Berkesch, Laura Felicia Matusevich, Uli Walther
We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct…
Singularities and holonomicity of binomial D-modules
Christine Berkesch Zamaere, Laura Felicia Matusevich, Uli Walther
We study binomial D-modules, which generalize A-hypergeometric systems. We determine explicitly their singular loci and provide three characterizations of their holonomicity. The f…
Local cohomology of logarithmic forms
Graham Denham, Hal Schenck, Mathias Schulze +2
Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic differential forms alon…
Resonance equals reducibility for A-hypergeometric systems
Mathias Schulze, Uli Walther
Classical theorems of Gel'fand et al., and recent results of Beukers, show that non-confluent Cohen-Macaulay A-hypergeometric systems have reducible monodromy representation if and…
Hypergeometric D-modules and twisted Gauss-Manin systems
Mathias Schulze, Uli Walther
The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module dir…
Irregularity of hypergeometric systems via slopes along coordinate subspaces
Mathias Schulze, Uli Walther
We study the irregularity sheaves attached to the -hypergeometric -module introduced by Gel'fand et al., where is pointed of full rank a…
Duality and monodromy reducibility of -hypergeometric systems
Uli Walther
We study -hypergeometric systems in the sense of Gelfand, Kapranov and Zelevinsky under two aspects: the structure of their holonomically dual system, and reducibility…