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Maximal degeneracy points of GKZ systems


Authors: S. Hosono, B. H. Lian and S.-T. Yau
Journal: J. Amer. Math. Soc. 10 (1997), 427-443
MSC (1991): Primary 14C30, 32G20
DOI: https://doi.org/10.1090/S0894-0347-97-00230-0
MathSciNet review: 1423031
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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: https://doi.org/10.1090/S0894-0347-97-00230-0
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
Article copyright: © Copyright 1997 by the authors

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