Systems of parameters and holonomicity of A-hypergeometric systems

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).