Castelnuovo-Mumford regularity of projective monomial varieties of codimension two
Let K be an algebraically closed field, and let V subset of P(K)(n+1) 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 Castel nuovo-Mumford regularity of V, reg(V), in terms of the reduced Grobner basis of I(V) with respect to the reverse lexicographic order. As a consequence, we show that reg (V) <= deg V - 1, where deg V is the degree of V, and characterize when equality holds. (c) 2006 Elsevier Ltd. All rights reserved.
castelnuovo-mumford regularity projective toric variety semigroup ring grobner basis simplicial affine semigroup monomial ideal of nested type