The regularity of a toric variety

JOURNAL OF ALGEBRA

卷:237

Article

Briales-Morales, E ; Pisón-Casares, P ; Vigneron-Tenorio, A

关键词: toric varieties;    syzygies;    simplicial complexes;    regularity;   

DOI  :  10.1006/jabr.2000.8582

来源: Elsevier

【 摘 要 】

We give a method for computing the degrees of the minimal syzygies of a toric variety by means of combinatorial techniques. Indeed, we complete the explicit description of the minimal free resolution of the associated semigroup algebra, using the simplicial representation of Koszul homology which appeared in A. Campillo and C. Marijuan (1991, Sem. Theor. Nombres Bordeaux 3, 249-260). As an application, we obtain an algorithm for computing the Castelnuovo-Mumford regularity of a projective toric variety. This regularity is explicitly bounded by means of the semigroup generators which parametrize the variety. (C) 2001 Academic Press.

【 授权许可】

Free