hypergeometric systems that come from geometry
Authors:
Alan Adolphson and Steven Sperber
Journal:
Proc. Amer. Math. Soc. 140 (2012), 20332042
MSC (2010):
Primary 33C70, 14F40; Secondary 52B20
Published electronically:
October 13, 2011
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Abstract: In recent work, Beukers characterized hypergeometric systems having a full set of algebraic solutions. He accomplished this by (1) determining which hypergeometric systems have a full set of polynomial solutions modulo for almost all primes 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 hypergeometric systems and de Rhamtype complexes, which leads to a determination of which hypergeometric 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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Additional Information
Alan Adolphson
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email:
adolphs@math.okstate.edu
Steven Sperber
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
sperber@math.umn.edu
DOI:
http://dx.doi.org/10.1090/S000299392011110736
PII:
S 00029939(2011)110736
Keywords:
$A$hypergeometric system,
de Rham cohomology
Received by editor(s):
December 9, 2010
Received by editor(s) in revised form:
January 24, 2011, and February 9, 2011
Published electronically:
October 13, 2011
Communicated by:
Lev Borisov
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
