We give a dimension formula for the space of logarithm-free series solutions to an A-hypergeometric (or a Gel’fand-Kapranov-Zelevinskiĭ (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 -modules.
"Logarithm-free A-hypergeometric series." Duke Math. J. 115 (1) 53 - 73, 1 October 2002. https://doi.org/10.1215/S0012-7094-02-11512-9