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Paper   IPM / M / 13374
School of Mathematics
  Title:   Cohen-Macaulayness and limit behavior of depth for powers of cover ideals
1.  M. R. Pournaki
2.  S. A. Seyed Fakhari
3.  S. Yassemi (Joint with A. Constantinescu and N. Terai)
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  43
  Year:  2015
  Pages:   143-157
  Supported by:  IPM
Let \mathbbK be a field, and let R=\mathbbK[x1,...,xn] be the polynomial ring over \mathbbK in n indeterminates x1,…,xn. Let G be a graph with vertex-set {x1,...,xn}, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J(k) and J[k], respectively. In this paper, we give necessary and sufficient conditions for R/Jk, R/J(k), and R/J[k] to be Cohen-Macaulay. We also study the limit behavior of the depths of these rings.

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