A Zariski theorem for monodromy of $A$-hypergeometric systems

TL;DR

This paper establishes conditions for the invariance of the monodromy group of $A$-hypergeometric systems under character modifications, utilizing a Zariski--Lefschetz theorem for principal $A$-determinants, advancing understanding of their algebraic structure.

Contribution

It introduces a Zariski--Lefschetz type theorem for principal $A$-determinants and applies it to determine invariance conditions of monodromy groups in $A$-hypergeometric systems.

Findings

Monodromy group invariance under character modifications

A Zariski--Lefschetz theorem for principal $A$-determinants

Conditions for monodromy invariance

Abstract

We give conditions under which the monodromy group of an $A$-hypergeometric system is invariant under modifications of the collection of characters $A$. The key ingredient is a Zariski--Lefschetz type theorem for principal $A$-determinants.