Hypergeometric Hodge modules

TL;DR

This paper studies the Hodge structures of GKZ-hypergeometric systems, revealing that their Hodge filtration aligns with the order filtration, and applies this to establish non-commutative Hodge structures in quantum cohomology.

Contribution

It demonstrates that the Hodge filtration on GKZ-hypergeometric D-modules matches the order filtration and proves a conjecture on non-commutative Hodge structures in quantum D-modules.

Findings

Hodge filtration equals the order filtration on GKZ-hypergeometric systems

Confirmed the existence of non-commutative Hodge structures in quantum D-modules

Provided new insights into the structure of mixed Hodge modules in hypergeometric systems

Abstract

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 suitable shift. As an application, we prove a conjecture on the existence of non-commutative Hodge structures on the reduced quantum D-module of a nef complete intersection inside a toric variety.