Matchings in simplicial complexes, circuits and toric varieties

摘要

Using a generalized notion of matching in a simplicial complex and circuits of vector configurations, we compute lower bounds for the minimum number of generators, the binomial arithmetical rank and the A-homogeneous arithmetical rank of a lattice ideal. Prime lattice ideals are toric ideals, i.e. the defining ideals of toric varieties. (c) 2006 Elsevier Inc. All rights reserved.