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arXiv · 1706.07603

Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals

Le Tuan Hoa·Tran Nam Trung
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Abstract

Let $I$ be a monomial ideal $I$ in a polynomial ring $R = k[x_1,...,x_r]$. In this paper we give an upper bound on $\overline{\dstab} (I)$ in terms of $r$ and the maximal generating degree $d(I)$ of $I$ such that $\depth R/\overline{I^n}$ is constant for all $n\geqslant \overline{\dstab}(I)$. As an application, we classify the class of monomial ideals $I$ such that $\overline{I^n}$ is Cohen-Macaulay for some integer $n\gg 0$.

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Le Tuan Hoa, Tran Nam Trung. 2017-06-23. Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals. https://doi.org/10.1007/s40306-017-0225-0

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