Bounds on the regularity and projective dimension of ideals associated to graphs

Details Bounds on the regularity and projective dimension of ideals associated to graphs Bounds on the regularity and projective dimension of ideals associated to graphs

2011-10-12

arxiv.org/abs/1110.2570v1

Mathematics

Commutative Algebra

Scientific paper

In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We also discuss and connect these results to more classical topics in commutative algebra.

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