Descripción: We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank. © 2004 Elsevier Inc. All rights reserved.

Descripción: We present examples that show that in dimension higher than one or codimension higher than two, there exist toric ideals IA such that no binomial ideal contained in IA and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations. © 2006 American Mathematical Society.