Vol. 276, No. 2, 2015

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ISSN: 0030-8730
Systems of parameters and holonomicity of $A$-hypergeometric systems

Christine Berkesch Zamaere, Stephen Griffeth and Ezra Miller

Vol. 276 (2015), No. 2, 281–286

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).

hypergeometric, differential operators, toric, holonomic
Mathematical Subject Classification 2010
Primary: 33C70
Secondary: 13N10, 14M25, 16S32, 33C99
Received: 10 January 2015
Revised: 19 February 2015
Accepted: 25 February 2015
Published: 15 July 2015
Christine Berkesch Zamaere
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States
Stephen Griffeth
Instituto de Matemática y Física
Universidad de Talca
Ezra Miller
Mathematics Department
Duke University
Durham, NC 27708
United States