Splittings of monomial ideals
Commutative Algebra
2009-02-14 v2 Combinatorics
Abstract
We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bipartite graphs. Finally, we consider the frequency with which one can find particular splittings of monomial ideals and raise questions about ideals whose resolutions are characteristic-dependent.
Cite
@article{arxiv.0807.2185,
title = {Splittings of monomial ideals},
author = {Christopher A. Francisco and Huy Tai Ha and Adam Van Tuyl},
journal= {arXiv preprint arXiv:0807.2185},
year = {2009}
}
Comments
minor changes: added Cor. 3.10 and some references. To appear in Proc. Amer. Math. Soc