A-HYPERGEOMETRIC SYSTEMS THAT COME FROM GEOMETRY

作者：Adolphson Alan^*; Sperber Steven

来源：Proceedings of the American Mathematical Society, 2012, 140(6): 2033-2042.

DOI：10.1090/S0002-9939-2011-11073-6

• A-hypergeometric system
• de Rham cohomology

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 A-hypergeometric systems come from geometry. We do not use the fact that the system is irreducible or find integral formulas for its solutions.

• 出版日期2012-6