Maximal Degeneracy Points of Gkz Systems

Motivated by mirror symmetry, we study certain integral repre-sentations of solutions to the Gel′fand-Kapranov-Zelevinsky (GKZ) hypergeo-metric system. Some of these solutions arise as period integrals for Calabi-Yaumanifolds in mirror symmetry. We prove that for a suitable compactificationof the parameter space, there exist certain special boundary points, whichwe called maximal degeneracy points, at which all solutions but one becomesingular. Department of Mathematics, Toyama University, Toyama 930, JapanE-mail address: [email protected] Department of Mathematics, Brandeis University, Waltham, Massachusetts 02154E-mail address: [email protected] Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use