Year: 2026
Type: preprint
Abstract: We study the behavior of Castelnuovo--Mumford regularity under integral closure. We prove a general cohomological criterion for the inequality $\operatorname{reg}(\overline J)\leq \operatorname{reg(J)}$, and in particular obtain it for every homogeneous ideal in a polynomial ring in at most three variables. The proof uses a high-degree comparison between $\overline J$ and its saturation. We also give a saturated monomial counterexample in four variables, showing that the three-variable result is sharp.
Source: arXiv (Cornell University)
Author: Misra, Soumyadeep
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161280106