Equality of ordinary and symbolic powers of Stanley-Reisner ideals

JOURNAL OF ALGEBRA

卷:328

Article

Ngo Viet Trung¹  Tran Manh Tuan¹ 

[1] Inst Math, Hanoi, Vietnam

关键词: Stanley-Reisner ideal;    Cohen-Macaulay ideal;    Symbolic power;    Vertex cover;    Ramsey graph;   

DOI  :  10.1016/j.jalgebra.2010.09.036

来源: Elsevier

【 摘 要 】

This paper studies properties of simplicial complexes Delta with the equality I-Delta((m)) = I-Delta(m) for a given m >= 2. The main results are combinatorial characterizations of such complexes in the two-dimensional case. It turns out that there exists only a finite number of complexes with this property and that these complexes can be described completely. As a consequence we are able to determine all complexes for which I-Delta(m) is Cohen-Macaulay for some m >= 2 In particular, there are complexes with I-Delta((2)) = I-Delta(2) or I-Delta((3)) but I-Delta((m)) not equal I-Delta(m) for all m >= 4 and that if I-Delta((m)) = I-Delta(m) for some m >= 4, then I-Delta((m)) = I-Delta(m) for all m >= 1. Similarly, there are complexes for which I-Delta(2), is Cohen-Macaulay but I-Delta(m) is not Cohen-Macaulay for all m >= 3 and if I-Delta(m) is Cohen-Macaulay for some m >= 3, then I-Delta is a complete intersection. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free