Computing Koszul Homology for Monomial Ideals
摘要
The Koszul homology of modules of the polynomial ring is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form where is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different Computer Algebra Systems (e.g. CoCoa, Singular, Macaulay), which compute minimal free resolutions of modules of the form with an ideal in , which include the case of being a monomial ideal as a particular one (a good review is given in \cite {Sie}). Our goal is to build algorithms especially teargeted to monomial ideals, taking into account the special combinatorial and structural properties of these ideals. This being a first goal, it is also a first step of an alternative approach to the computation of the Koszul homology and minimal free resolutions of polynomial ideals.
引用
@article{arxiv.math/0605325,
title = {Computing Koszul Homology for Monomial Ideals},
author = {Eduardo Saenz de Cabezon},
journal= {arXiv preprint arXiv:math/0605325},
year = {2007}
}
备注
Appears in Proceedings of the 10th Rhine Workshop on Computer Algebra