Cohen-Macaulayness for symbolic power ideals of edge ideals

JOURNAL OF ALGEBRA

卷:347

Article

Rinaldo, Giancarlo²  Terai, Naoki³  Yoshida, Ken-ichi¹ 

[1] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan

[2] Univ Messina, Dipartimento Matemat, I-98166 Messina, Italy

[3] Saga Univ, Dept Math, Fac Culture & Educ, Saga 8408502, Japan

关键词: Edge ideal;    Complete intersection;    Cohen-Macaulay;    FLC;    Symbolic powers;    Polarization;    Simplicial complex;   

DOI  :  10.1016/j.jalgebra.2011.09.007

来源: Elsevier

【 摘 要 】

Let S = K[x(1), ..., x(n)] be a polynomial ring over a field K. Let l(G) subset of S denote the edge ideal of a graph G. We show :hat the lth symbolic power l(G)((l)) is a Cohen-Macaulay ideal i.e., S/I(G)((l)) is Cohen-Macaulay) for some integer l >= 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)((l)) are Cohen-Macaulay ideals. Similarly, we characterize graphs G for which S/I((G)((l)) has (FLC). As an application, we show that an edge ideal I(G) is complete intersection provided that S/I(G)(l) is Cohen-Macaulay for some integer l >= 3. This strengthens the main theorem in Crupi et al. (2010) [3]. (C) 2011 Elsevier Inc. All rights reserved.

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