Resumen de Minimal generating sets of lattice ideals

Hara Charalambous, Apostolos Thoma, Marius Vladoiu

• Let ?⊂ℤ? be a lattice and ??=⟨??−??: ?−?∈?⟩ be the corresponding lattice ideal in ?[?1,…,??] , where ? is a field. In this paper we describe minimal binomial generating sets of ?? and their invariants. We use as a main tool a graph construction on equivalence classes of fibers of ?? . As one application of the theory developed we characterize binomial complete intersection lattice ideals, a longstanding open problem in the case of non-positive lattices.