Resumen de Set-theoretic complete intersections on binomials, the simplicial toric case

Margherita Barile, Marcel Morales , Apostolos Thoma

• Let V be a simplicial toric variety of codimension r over a field of any characteristic. We completely characterize the implicial toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that: 1. In characteristic zero, V is a set-theoretic complete intersection on binomials if and only jf V is a. complete intersection.  Moreover, if F1,…,Fr; are binomials such that I(V)= rad( F1, . .. ,Fr), th en I(V) = (F1, ... ,Fr). We also get a geometric proof of some of the results in [9] characterizing complete intersections by gluing; semigroups. 2. In positive characteristic p, V is a set-theoretic complete intersection on binomials if and only if V is complete 1y p-glued. These results improve and complete all known results on these topics.