Resumen de Minimal generating sets of lattice ideals

Hara Charalambous, Apostolos Thoma, Marius Vladoiu

• Let L\subset \mathbb {Z}^n be a lattice and I_L=\langle x^{\mathbf {u}}-x^{\mathbf {v}}:\ {\mathbf {u}}-{\mathbf {v}}\in L\rangle be the corresponding lattice ideal in \Bbbk [x_1,\ldots , x_n], where \Bbbk is a field. In this paper we describe minimal binomial generating sets of I_L and their invariants. We use as a main tool a graph construction on equivalence classes of fibers of I_L. 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.