Cohen--Macaulaynees for symbolic power ideals of edge ideals

Details Cohen--Macaulaynees for symbolic power ideals of edge ideals Cohen--Macaulaynees for symbolic power ideals of edge ideals

2012-03-09

arxiv.org/abs/1203.1967v1

Journal of Algebra 347 (2011) 405-430

Mathematics

Commutative Algebra

The final version have been published

Scientific paper

Let $S = K[x_1,..., x_n]$ be a polynomial ring over a field $K$. Let $I(G) \subseteq S$ denote the edge ideal of a graph $G$. We show that the $\ell$th symbolic power $I(G)^{(\ell)}$ is a Cohen-Macaulay ideal (i.e., $S/I(G)^{(\ell)}$ is Cohen-Macaulay) for some integer $\ell \ge 3$ if and only if $G$ is a disjoint union of finitely many complete graphs. When this is the case, all the symbolic powers $I(G)^{(\ell)}$ are Cohen-Macaulay ideals. Similarly, we characterize graphs $G$ for which $S/I(G)^{(\ell)}$ has (FLC). As an application, we show that an edge ideal $I(G)$ is complete intersection provided that $S/I(G)^{\ell}$ is Cohen-Macaulay for some integer $\ell \ge 3$. This strengthens the main theorem in [Effective Cowsik-Nori theorem for edge ideals by M.Crupi, G.Rinaldo, N.Terai, and K.Yoshida, Comm. Alg. 38 (2010), 3347-3357].

Affiliated with

Also associated with

No associations

Rating

Cohen--Macaulaynees for symbolic power ideals of edge ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cohen--Macaulaynees for symbolic power ideals of edge ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cohen--Macaulaynees for symbolic power ideals of edge ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-301352