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Maximal degeneracy points of GKZ systems. (English) Zbl 0874.32007
Summary: 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.

MSC:
32G20 Period matrices, variation of Hodge structure; degenerations
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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