2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60658We give a dimension formula for the space of logarithm-free series solutions to an A-hypergeometric (or a 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.20 pages, 2 figures, LaTeX2eAlgebraic GeometryCommutative Algebra33C70; 14M25; 13N10; 16S32text