j-multiplicity and depth of associated graded modules

2011/01/12 by Claudia Polini, Yu Xie, Polini, Claudia +1 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1101.2281

arxiv created 2011/01/12 · openalex publication_date 2011/01/12 · arxiv updated 2011/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a Noetherian local ring. We define the minimal j-multiplicity and almost minimal j-multiplicity of an arbitrary R-ideal on any finite R-module. For any ideal I with minimal j-multiplicity or almost minimal j-multiplicity on a Cohen-Macaulay module M, we prove that under some residual assumptions, the associated graded module \rm gr_I(M) is Cohen-Macaulay or almost Cohen-Macaulay, respectively. Our work generalizes the results for minimal multiplicity and almost minimal multiplicity obtained by Sally, Rossi, Valla, Wang, Huckaba, Elias, Corso, Polini, and VazPinto.

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