Logarithm-free A-hypergeometric series

摘要

We give a dimension formula for the space of logarithm-free series solutions to an A-hypergeornetric (or a Gel'fand-Kapranov-Zelevinskii (GKZ) hypergeometric) system. In the case where the convex hull spanned by A is a simplex, we give a rank formula for the system, characterize the exceptional set, and prove the equivalence of the Cohen-Macaulayness of the toric variety defined by A with the emptiness of the exceptional set. Furthermore, we classify A-hypergeometric systems as analytic D-modules. [References: 9]