Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules

Abstract

We endow certain GKZ-hypergeometric systems with a natural structure of a mixed Hodge module, which is compatible with the mixed Hodge module structure on the Gauβ-Manin system of an associated family of Laurent polynomials. As an application we show that the underlying perverse sheaf of a GKZ-system with rational parameter has quasi-unipotent local monodromy. © 2014 Foundation Compositio Mathematica.