Resolutions of facet ideals
Commutative Algebra
2007-05-23 v1
Abstract
In this paper we study the resolution of a facet ideal associated with a special class of simplicial complexes introduced by S. Faridi. These simplicial complexes are called trees, and are a generalization (to higher dimensions) of the concept of a tree in graph theory. We show that the Koszul homology of the facet ideal I of a tree is generated by the homology classes of monomial cycles, determine the projective dimension and the regularity of I if the tree is 1-dimensional, show that the graded Betti numbers of I satisfy an alternating sum property if the tree is connected in codimension 1, and classify all trees whose facet ideal has a linear resolution.
Cite
@article{arxiv.math/0307241,
title = {Resolutions of facet ideals},
author = {Xinxian Zheng},
journal= {arXiv preprint arXiv:math/0307241},
year = {2007}
}
Comments
22 pages