TY - JOUR

T1 - A-hypergeometric systems that come from geometry

AU - Adolphson, Alan

AU - Sperber, Steven

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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U2 - 10.1090/S0002-9939-2011-11073-6

DO - 10.1090/S0002-9939-2011-11073-6

M3 - Article

AN - SCOPUS:84857250717

VL - 140

SP - 2033

EP - 2042

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -