Splittings of monomial ideals

Details Splittings of monomial ideals Splittings of monomial ideals

2008-07-14

arxiv.org/abs/0807.2185v2

Mathematics

Commutative Algebra

minor changes: added Cor. 3.10 and some references. To appear in Proc. Amer. Math. Soc

Scientific paper

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.

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