Maximal degeneracy points of GKZ systems |
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Authors: | S. Hosono B. H. Lian S.-T. Yau |
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Affiliation: | Department of Mathematics, Toyama University, Toyama 930, Japan ; Department of Mathematics, Brandeis University, Waltham, Massachusetts 02154 ; Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 |
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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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Keywords: | Mirror symmetry, hypergeometric systems, period integrals, Calabi-Yau manifolds, toric varieties, compactification, indicial ideal, Gr" obner bases |
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