Perverse schobers and GKZ systems

TL;DR

This paper constructs a categorification of GKZ hypergeometric systems using perverse schobers, linking geometric representation theory with hypergeometric differential equations, especially in the context of toric varieties and hyperplane arrangements.

Contribution

It introduces a new categorification of GKZ systems via perverse schobers, extending previous work on stringy K"ahler moduli spaces and hyperplane arrangements.

Findings

Categorification of GKZ hypergeometric systems for non-resonant parameters.

Description of monodromy for quasi-symmetric GKZ systems.

Connection between perverse schobers and hypergeometric differential equations.

Abstract

Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy K\"ahler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric representation of a reductive group. When the group is a torus the SKMS corresponds to the complement of the GKZ discriminant locus (which is a hyperplane arrangement in the quasi-symmetric case shown by Kite). We show here that a suitable variation of the perverse schober we constructed provides a categorification of the associated GKZ hypergeometric system in the case of non-resonant parameters. As an intermediate result we give a description of the monodromy of such "quasi-symmetric" GKZ hypergeometric systems.