Resumen de Castelnuovo¿Mumford regularity of projective monomial varieties of codimension two

Marcel Morales , Philippe Giménez , María Isabel Bermejo Díaz

• Let K be an algebraically closed field, and let be a projective monomial variety of codimension two with n=2, i.e., a projective toric variety of codimension two whose homogeneous coordinate ring is a simplicial semigroup ring. We give an explicit formula for the Castelnuovo¿Mumford regularity of , , in terms of the reduced Gröbner basis of with respect to the reverse lexicographic order. As a consequence, we show that , where is the degree of , and characterize when equality holds.