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

2025/07/16 by Omkar Javadekar, Javadekar, Omkar
Computer Science · Mathematics · #13A02 #13B22 #13D02 #13F55 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.12178

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Let S = k[x₁, …, x_n], 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.

Citations

• Regularity of integral closures of edge ideals of weighted oriented graphs
• Some inequalities regarding the regularity of powers of monomial ideals
• Differences in regularities of a power and its integral closure and symbolic power
• Castelnuovo--Mumford Regularity and Log-canonical Thresholds

Related

• Some inequalities regarding the regularity of powers of monomial ideals
• The regularity of monomial ideals and their integral closures
• Stanley depth of the integral closure of monomial ideals
• Regularity jumps for powers of ideals
• On the Castelnuovo-Mumford regularity of ideals, in dimension 2