2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76105We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals I_A such that no binomial ideal contained in I_A 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.to appear in Proc. Am. Math. SocCommutative AlgebraAlgebraic Geometrytext