15 citations · 66 across the 22 of their papers we have counts for
24 papers · 1 filter
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…
Duality theory of tautological systems
Paul Görlach, Christian Sevenheck
We discuss the holonomic dual of tautological systems, with a view towards applications to linear free divisors and to homogeneous spaces. As a technical tool, we consider a Cheval…
Irregular Hodge numbers of Frenkel--Gross connections
Yichen Qin, Christian Sevenheck, Peter Spacek
Frenkel and Gross constructed a family of connections on , for almost simple groups and their representations. In this article, we c…
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…
Betti structures of hypergeometric equations
Davide Barco, Marco Hien, Andreas Hohl +1
We study Betti structures in the solution complexes of confluent hypergeometric equations. We use the framework of enhanced ind-sheaves and the irregular Riemann-Hilbert correspond…
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…
Hodge ideals of free divisors
Alberto Castaño Domínguez, Luis Narváez Macarro, Christian Sevenheck
We consider the Hodge filtration on the sheaf of meromorphic functions along free divisors for which the logarithmic comparison theorem holds. We describe the Hodge filtration step…
Tautological systems and free divisors
Luis Narváez Macarro, Christian Sevenheck
We introduce tautological system defined by prehomogenous actions of reductive algebraic groups. If the complement of the open orbit is a linear free divisor satisfying a certain f…
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,…
Irregular Hodge filtration of some confluent hypergeometric systems
Alberto Castaño Domínguez, Christian Sevenheck
We determine the irregular Hodge filtration, as introduced by Sabbah, for the purely irregular hypergeometric -modules. We obtain in particular a formula for the irreg…
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…
Duality of Gauss-Manin systems associated to linear free divisors
Christian Sevenheck
We investigate differential systems occurring in the study of particular non-isolated singularities, the so-called linear free divisors. We obtain a duality theorem for these D-mod…
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…
Bernstein polynomials and spectral numbers for linear free divisors
Christian Sevenheck
We discuss Bernstein polynomials of reductive linear free divisors. We define suitable Brieskorn lattices for these non-isolated singularities, and show the analogue of Malgrange's…
Twistor structures, tt*-geometry and singularity theory
Claus Hertling, Christian Sevenheck
We give an overview on the tt*-geometry defined for isolated hypersurface singularities and tame functions via Brieskorn lattices. We discuss nilpotent orbits in this context, as w…
Limits of families of Brieskorn lattices and compactified classifying spaces
Claus Hertling, Christian Sevenheck
We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated vari…
Linear free divisors and Frobenius manifolds
Ignacio de Gregorio, David Mond, Christian Sevenheck
We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauss-Manin system associated to these functions, and prove the existence of a…
Curvature of classifying spaces for Brieskorn lattices
Claus Hertling, Christian Sevenheck
We study tt*-geometry on the classifying space for regular singular TERP-structures, e.g., Fourier-Laplace transformations of Brieskorn lattices of isolated hypersurface singularit…
Nilpotent orbits of a generalization of Hodge structures
Claus Hertling, Christian Sevenheck
We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on P^1, with additi…
Rigid and Complete Intersection Lagrangian Singularities
Christian Sevenheck, Duco van Straten
In this article we prove a rigidity theorem for lagrangian singularities by studying the local cohomology of the lagrangian de Rham complex that was introduced in math.AG/0002083.…
Deformation of singular lagrangian subvarieties
Duco van Straten, Christian Sevenheck
We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Exampl…