Systems of parameters and holonomicity of A-hypergeometric systems

TL;DR

This paper provides an elementary proof that A-hypergeometric systems are holonomic, regardless of singularity behavior, and demonstrates they form holonomic families over parameter spaces, simplifying and extending previous results.

Contribution

It offers a new, straightforward proof of holonomicity for A-hypergeometric systems without singularity restrictions and confirms their holonomic family structure over parameters.

Findings

Elementary proof of holonomicity without singularity restrictions

Confirmation that A-hypergeometric systems form holonomic families

Simplification of previous proofs by Gelfand, Gelfand, and others

Abstract

The main result is an elementary proof of holonomicity for A-hypergeometric systems, with no requirements on the behavior of their singularities, originally due to Adolphson [Ado94] after the regular singular case by Gelfand and Gelfand [GG86]. Our method yields a direct de novo proof that A-hypergeometric systems form holonomic families over their parameter spaces, as shown by Matusevich, Miller, and Walther [MMW05].