“School of Mathematics”
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| Paper IPM / M / 13374 |
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| Abstract: | |||||||
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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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