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This is a Quantitative Study study.

October 15, 2025Open Access

A comparison of the regularity of certain classes of monomial ideals and their integral closures

Key Points

The regularity of the integral closure is always less than or equal to that of the original ideal.
This study proves a conjecture by Küronya and Pintye regarding regularity for specific monomial ideals.
We focused on different classes of monomial ideals to validate the conjecture's applicability.
Understanding these ideals helps in broader algebraic geometry contexts and can influence future research directions.

Abstract

Let S = kx₁, , xₙ, I be an ideal of S, and I denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal I of S, the inequality reg (I) reg (I) holds, where reg (\_) denotes the Castelnuovo-Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals.

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Cite This Study

Omkar Javadekar (Wed,) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba0635565f https://doi.org/https://doi.org/10.48550/arxiv.2507.12178

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