Bounds on the Castelnuovo-Mumford Regularity in dimension two

2024/04/02 by Mandal, Mousumi, Priya, Shruti · 1 citation
#13A30 #13D40 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.01684

Abstract

Consider a Cohen-Macaulay local ring (R,\mathfrak m) with dimension d≥ 2, and let I ⊆ R be an \mathfrak m-primary ideal. Denote r_J(I) as the reduction number of I with respect to a minimal reduction J of I, and ρ(I) as the stability index of the Ratliff-Rush filtration with respect to I. In this paper, we derive a bound on ρ(I) in terms of the Hilbert coefficients and r_J(I). In the case of two-dimensional Cohen-Macaulay local rings, the established bound on ρ(I) consequently leads to a bound on the Castelnuovo-Mumford regularity of the associated graded ring of I.

Cited by

• Bounds on the second Hilbert coefficient and the depth of the associated graded ring

Related

• Bounding reduction number and the Hilbert coefficients of filtration
• A note on Ratliff-Rush filtration, reduction number and postulation number of \mathfrak m-primary ideals
• Ratliff-Rush ideal and reduction numbers
• Castelnuovo-Mumford Regularity and finiteness of Hilbert Functions
• Ratliff-Rush filtration, Hilbert coefficients and the reduction number of integrally closed ideals