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Maximal degeneracy points of GKZ systems
Author(s):
S.
Hosono;
B.
H.
Lian;
S.-T.
Yau
Journal:
J. Amer. Math. Soc.
10
(1997),
427-443.
MSC (1991):
Primary 14C30, 32G20
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Abstract:
Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel´fand-Kapranov-Zelevinsky (GKZ) hypergeometric system. Some of these solutions arise as period integrals for Calabi-Yau manifolds in mirror symmetry. We prove that for a suitable compactification of the parameter space, there exist certain special boundary points, which we called maximal degeneracy points, at which all solutions but one become singular.
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Additional Information:
S.
Hosono
Affiliation:
Department of Mathematics, Toyama University, Toyama 930, Japan
Email:
hosono@sci.toyama-u.ac.jp
B.
H.
Lian
Affiliation:
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02154
Email:
lian@max.math.brandeis.edu
S.-T.
Yau
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
DOI:
10.1090/S0894-0347-97-00230-0
PII:
S 0894-0347(97)00230-0
Keywords:
Mirror symmetry,
hypergeometric systems,
period integrals,
Calabi-Yau manifolds,
toric varieties,
compactification,
indicial ideal,
Gr\"obner bases
Received by editor(s):
May 28, 1996
Received by editor(s) in revised form:
November 13, 1996
Copyright of article:
Copyright
1997,
by the authors
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