Multiplicities of weakly graded families of ideals

2024/11/07 by Parangama Sarkar, Sarkar, Parangama
Mathematics · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2411.04831

Abstract

In this article, we extend the notion of multiplicity for weakly graded families of ideals which are bounded below linearly. In particular, we show that the limit e_W(\mathfrakI):=lim_n→∞d!(ℓ_R(R/I_n))/(n^d) exists where \mathfrak I=\I_n\ is a bounded below linearly weakly graded families of ideals in a Noetherian local ring (R,\mathfrak m) of dimension d≥ 1 with dim(N(R))

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