A comparison of the regularity of certain classes of monomial ideals and their integral closures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912485974474752 |
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| author | Javadekar, Omkar |
| author_facet | Javadekar, Omkar |
| contents | Let $S = \mathsf{k}[x_1, \ldots, x_n]$, $I$ be an ideal of $S$, and $\bar{I}$ denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal $I$ of $S$, the inequality $\operatorname{reg}(\bar{I}) \leq \operatorname{reg}(I)$ holds, where $\operatorname{reg}(\_)$ denotes the Castelnuovo-Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A comparison of the regularity of certain classes of monomial ideals and their integral closures Javadekar, Omkar Commutative Algebra 13D02, 13A02, 13B22, 13F55 Let $S = \mathsf{k}[x_1, \ldots, x_n]$, $I$ be an ideal of $S$, and $\bar{I}$ denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal $I$ of $S$, the inequality $\operatorname{reg}(\bar{I}) \leq \operatorname{reg}(I)$ holds, where $\operatorname{reg}(\_)$ denotes the Castelnuovo-Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals. |
| title | A comparison of the regularity of certain classes of monomial ideals and their integral closures |
| topic | Commutative Algebra 13D02, 13A02, 13B22, 13F55 |
| url | https://arxiv.org/abs/2507.12178 |