𝐴-hypergeometric systems that come from geometry
Alan Adolphson, Steven Sperber · Proceedings of the American Mathematical Society · 2011
In recent work, Beukers characterized A {A} -hypergeometric systems having a full set of algebraic solutions. He accomplished this by (1) determining which A {A} -hypergeometric systems have a full set of polynomial solutions modulo p p for almost all primes p 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 A -hypergeometric systems and de Rham-type complexes, which leads to a determination of which A A -hypergeometric systems come from geometry. We do not use the fact that the system is irreducible or find integral formulas for its solutions.