#### Vol. 276, No. 2, 2015

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

### Christine Berkesch Zamaere, Stephen Griffeth and Ezra Miller

Vol. 276 (2015), No. 2, 281–286
##### 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