Asymptotic colengths for families of ideals: an analytic approach

2024/10/15 by Das, Sudipta, Meng, Cheng · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.11991

Abstract

This article focuses on the existence of asymptotic colengths for families of \fm_R-primary ideals in a Noetherian local ring (R,\fm). In any characteristic, we generalize graded families to weakly graded families of ideals, and in prime characteristic, we explore various families such as weakly p-families and weakly inverse p-families. The main contribution of this paper is providing a unified analytic method to prove the existence of limits. Additionally, we establish Brunn-Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals.

Cited by

• Generalized Hilbert-Kunz Multiplicity for Families of Ideals

Related

• Growth of multiplicities of graded families of ideals
• Multiplicities of weakly graded families of ideals
• Asymptotic Multiplicities
• Local Okounkov bodies and limits in prime characteristic
• Degree functions of graded families of ideals