an:01007816
Zbl 0874.32007
Hosono, S.; Lian, B. H.; Yau, S.-T.
Maximal degeneracy points of GKZ systems
EN
J. Am. Math. Soc. 10, No. 2, 427-443 (1997).
00040617
1997
j
32G20 14C30 14M25
Mirror symmetry; hypergeometric systems; period integrals; Calabi-Yau manifolds; toric varieties; compactification; indicial ideal; Gr??bner bases
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.