Hypergeometric Functions for Projective Toric Curves
arXiv:1412.3957
Abstract
We produce a decomposition of the parameter space of the -hypergeometric system associated to a projective monomial curve as a union of an arrangement of lines and its complement, in such a way that the analytic behavior of the solutions of the system is explicitly controlled within each term of the union.
27 pages and 3 figures. Expanded introduction. Proof of Theorem 2.1 removed, Section 2 merged with the section on resonant parameters. Theorem 3.3 generalized to a space of arbitrary dimension. New Theorem 3.4 and Corollary 3.5. Proposition 4.2 and Corollary 4.3 from version 1 are false, and have been removed. Proposition 4.4 now combines what used to be Corollary 5.3 and Proposition 5.4