Twisted GKZ hypergeometric functions and relative cohomology

TL;DR

This paper explores the properties of GKZ hypergeometric $ extit{D}$-modules associated with cyclic covers of toric varieties and identifies their Riemann--Hilbert counterparts, extending previous research.

Contribution

It introduces a new analysis of GKZ hypergeometric modules related to cyclic covers and establishes their Riemann--Hilbert correspondence, expanding the theoretical framework.

Findings

Extended the understanding of GKZ hypergeometric $ extit{D}$-modules

Established the Riemann--Hilbert correspondence for these modules

Generalized previous results to cyclic covers of toric varieties

Abstract

We investigate the GKZ $A$-hypergeometric $\mathscr{D}$-modules, introduced by Gel'fand, Kapranov, and Zelevinskii, arising from cyclic covers of toric varieties and find its Riemann--Hilbert partner. This extends our earlier results in arXiv:1902.01536.