27 citations · 86 across the 15 of their papers we have counts for
18 papers
Tautological systems and local cohomology
Paul Görlach, Thomas Reichelt, Christian Sevenheck +1
We discuss the connections between tautological systems and the local cohomology of cones over homogeneous spaces. We study a derived version of tautological systems, related to th…
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…
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…
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…
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…
Examples of hypergeometric twistor -modules
Alberto Castaño Domínguez, Thomas Reichelt, Christian Sevenheck
We show that certain one-dimensional hypergeometric differential systems underlie objects of the category of irregular mixed Hodge modules, which was recently introduced by Sabbah,…
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…
Logarithmic degenerations of Landau-Ginzburg models for toric orbifolds and global tt^* geometry
Etienne Mann, Thomas Reichelt
We discuss the behavior of Landau-Ginzburg models for toric orbifolds near the large volume limit. This enables us to express mirror symmetry as an isomorphism of Frobenius manifol…
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…
Hypergeometric Hodge modules
Thomas Reichelt, Christian Sevenheck
We consider mixed Hodge module structures on GKZ-hypergeometric differential systems. We show that the Hodge filtration on these D-modules is given by the order filtration, up to s…
Non-affine Landau-Ginzburg models and intersection cohomology
Thomas Reichelt, Christian Sevenheck
We construct Landau-Ginzburg models for numerically effective complete intersections in toric manifolds as partial compactifications of families of Laurent polynomials. We show a m…
A comparison theorem between Radon and Fourier-Laplace transforms for D-modules
Thomas Reichelt
We prove a comparison theorem between the d-plane Radon transform and the Fourier-Laplace transform for D-modules. This generalizes results of Brylinski and d'Agnolo-Eastwood.
Laurent Polynomials, GKZ-hypergeometric Systems and Mixed Hodge Modules
Thomas Reichelt
Given a family of Laurent polynomials, we will construct a morphism between its (proper) Gauss-Manin system and a direct sum of associated GKZ systems. The kernel and cokernel of t…
Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules
Thomas Reichelt, Christian Sevenheck
We describe mirror symmetry for weak toric Fano manifolds as an equivalence of D-modules equipped with certain filtrations. We discuss in particular the logarithmic degeneration be…
A construction of Frobenius manifolds with logarithmic poles and applications
Thomas Reichelt
A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a gene…