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arXiv · 2412.14904

On the set of associated radicals of powers of monomial ideals

Nguyen Thu Hang·Truong Thi Hien
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Abstract

Let $I$ be a monomial ideal in a polynomial ring. In this paper, we study the asymptotic behavior of the set of associated radical ideals of the (symbolic) powers of $I$. We show that both $\asr(I^s)$ and $\asr(I^{(s)})$ need not stabilize for large value of $s$. In the case $I$ is a square-free monomial ideal, we prove that $\asr(I^{(s)})$ is constant for $s$ large enough. Finally, if $I$ is the cover ideal of a balanced hypergraph, then $\asr(I^s)$ monotonically increases in $s$.

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Nguyen Thu Hang, Truong Thi Hien. 2024-12-19. On the set of associated radicals of powers of monomial ideals. https://arxiv.org/abs/2412.14904

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