Asymptotic colengths for families of ideals: an analytic approach

Fuente: arXiv
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Main Authors: Das, Sudipta, Meng, Cheng
Format: Preprint
Published: 2024
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author Das, Sudipta
Meng, Cheng
author_facet Das, Sudipta
Meng, Cheng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_11991
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Asymptotic colengths for families of ideals: an analytic approach
Das, Sudipta
Meng, Cheng
Commutative Algebra
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.
title Asymptotic colengths for families of ideals: an analytic approach
topic Commutative Algebra
url https://arxiv.org/abs/2410.11991