Details:
Title  Castelnuovo–Mumford regularity of projective monomial varieties of codimension two  Author(s)  Isabel Bermejo, Philippe Gimenez, Marcel Morales  Type  Article in Journal  Abstract  Let K be an algebraically closed field, and let V ⊂ 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 Castelnuovo–Mumford regularity of V , reg ( V ) , in terms of the reduced Gröbner 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.  Keywords  Castelnuovo–Mumford regularity, Projective toric variety, Semigroup ring, Simplicial affine semigroup, Monomial ideal of nested type, Gröbner basis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717106000514 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  10  Pages  1105  1124  Year  2006  Edition  0  Translation 
No  Refereed 
No 
