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TitleCastelnuovo–Mumford regularity of projective monomial varieties of codimension two
Author(s) Isabel Bermejo, Philippe Gimenez, Marcel Morales
TypeArticle in Journal
AbstractLet 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.
KeywordsCastelnuovo–Mumford regularity, Projective toric variety, Semigroup ring, Simplicial affine semigroup, Monomial ideal of nested type, Gröbner basis
URL http://www.sciencedirect.com/science/article/pii/S0747717106000514
JournalJournal of Symbolic Computation
Pages1105 - 1124
Translation No
Refereed No