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arXiv · 2309.05011

Depth of powers of edge ideals of Cohen-Macaulay trees

Nguyen Thu Hang·Truong Thi Hien·Thanh Vu
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Abstract

Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{d},y_1,\ldots,y_d]$. We prove that for all $t \ge 1$, $$\operatorname{depth} (S/I^t) = \operatorname{max} \{d -t + 1, 1 \}.$$

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Nguyen Thu Hang, Truong Thi Hien, Thanh Vu. 2023-09-10. Depth of powers of edge ideals of Cohen-Macaulay trees. https://arxiv.org/abs/2309.05011

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