A counterexample to a conjecture of Küronya and Pintye on regularity and integral closure
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911683312615424 |
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| author | Misra, Soumyadeep |
| author_facet | Misra, Soumyadeep |
| contents | We exhibit an equigenerated monomial ideal $I\subseteq K[x,y,z,w]$ with $\operatorname{reg}(\overline{I})>\operatorname{reg}(I)$. The ideal $I$ is generated in degree 4 and satisfies $\operatorname{reg}(I)=4$, while its integral closure $\overline{I}$ has a minimal generator of degree 5 and satisfies $\operatorname{reg}(\overline{I})=5$. This gives a counterexample to the polynomial-ring formulation of the Küronya--Pintye conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13879 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A counterexample to a conjecture of Küronya and Pintye on regularity and integral closure Misra, Soumyadeep Commutative Algebra We exhibit an equigenerated monomial ideal $I\subseteq K[x,y,z,w]$ with $\operatorname{reg}(\overline{I})>\operatorname{reg}(I)$. The ideal $I$ is generated in degree 4 and satisfies $\operatorname{reg}(I)=4$, while its integral closure $\overline{I}$ has a minimal generator of degree 5 and satisfies $\operatorname{reg}(\overline{I})=5$. This gives a counterexample to the polynomial-ring formulation of the Küronya--Pintye conjecture. |
| title | A counterexample to a conjecture of Küronya and Pintye on regularity and integral closure |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2605.13879 |