Systems of parameters and holonomicity of $A$-hypergeometric systems

Christine Berkesch Zamaere, Stephen Griffeth and Ezra Miller

Vol. 276 (2015), No. 2, 281–286

DOI: 10.2140/pjm.2015.276.281

Abstract

We give an elementary proof of holonomicity for $A$-hypergeometric systems, with no requirements on the behavior of their singularities, a result originally due to Adolphson (1994) after the regular singular case by Gelfand and Gelfand (1986). 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 (2005).

Keywords

hypergeometric, differential operators, toric, holonomic

Mathematical Subject Classification 2010

Primary: 33C70

Secondary: 13N10, 14M25, 16S32, 33C99

Milestones

Received: 10 January 2015

Revised: 19 February 2015

Accepted: 25 February 2015

Published: 15 July 2015