A-hypergeometric systems that come from geometry

Alan Adolphson, Steven Sperber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In recent work, Beukers characterized A-hypergeometric systems having a full set of algebraic solutions. He accomplished this by (1) determining which A-hypergeometric systems have a full set of polynomial solutions modulo p for almost all primes p and (2) showing that these systems come from geometry. He then applied a fundamental theorem of N. Katz, which says that such systems have a full set of algebraic solutions. In this paper we establish some connections between nonresonant A-hypergeometric systems and de Rham-type complexes, which leads to a determination of which Ahypergeometric systems come from geometry. We do not use the fact that the system is irreducible or find integral formulas for its solutions.

Original languageEnglish (US)
Pages (from-to)2033-2042
Number of pages10
JournalProceedings of the American Mathematical Society
Volume140
Issue number6
DOIs
StatePublished - 2012

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