Laurent Polynomials, GKZ-hypergeometric Systems and Mixed Hodge Modules

Abstract

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 this morphism are very simple and consist of free O-modules. The result above enables us to put a mixed Hodge module structure on certain classes of GKZ systems and shows that they have quasi-unipotent monodromy.

34 pages

References in corpus (3)

• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Hypergeometric D-modules and twisted Gauss-Manin systems
• Hodge theory and unitary representations of reductive Lie groups

Cited by in corpus (9)

• Algebraic aspects of hypergeometric differential equations
• Irregular Hodge filtration of some confluent hypergeometric systems
• Examples of hypergeometric twistor $\mathcal{D}$-modules
• $A$-Hypergeometric Modules and Gauss--Manin Systems
• Dualizing, projecting, and restricting GKZ systems
• On the $b$-functions of hypergeometric systems
• $A$-hypergeometric systems and relative cohomology
• Tautological systems and free divisors
• A description of monodromic mixed Hodge modules