On the set of associated radicals of powers of monomial ideals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912161376239616 |
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| author | Hang, Nguyen Thu Hien, Truong Thi |
| author_facet | Hang, Nguyen Thu Hien, Truong Thi |
| contents | 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 $s$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the set of associated radicals of powers of monomial ideals Hang, Nguyen Thu Hien, Truong Thi Commutative Algebra 13A15, 13C13 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 $s$. |
| title | On the set of associated radicals of powers of monomial ideals |
| topic | Commutative Algebra 13A15, 13C13 |
| url | https://arxiv.org/abs/2412.14904 |