𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Syzygies of affine toric varieties

✍ Scribed by Antonio Campillo; Philippe Gimenez


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
996 KB
Volume
225
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis


We give a method for computing the syzygies of the coordinate ring R of an affine toric variety. We show how the method works for dimension one and two cases, Cohen-Macaulay semigroups, and for computing minimal generators of the defining ideal. We show how to compute the depth of R and generalize a criterion for Cohen-Macaulayness.


πŸ“œ SIMILAR VOLUMES


Families of toric varieties
✍ Mihai Halic πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 351 KB

## Abstract The goal of this article is to construct families of complete toric varieties over arbitrary bases, and to compute the cohomology of the total space. (Β© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Regularity of a Toric Variety
✍ E Briales-Morales; P PisΓ³n-Casares; A Vigneron-Tenorio πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 164 KB

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 ap

Effective equidimensional decomposition
✍ Gabriela Jeronimo; Juan Sabia πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 169 KB

In this paper we present a probabilistic algorithm which computes, from a ΓΏnite set of polynomials deΓΏning an algebraic variety V , the decomposition of V into equidimensional components. If V is deΓΏned by s polynomials in n variables of degrees bounded by an integer d ΒΏ n and V = r '=0 V ' is the e