j-Multiplicity and depth of associated graded modules

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• 作者：Claudia Polini^a ; ¹ ; ^{cpolini@nd.edu} ; Yu Xie^b ; ^yxie@gsu.edu
• 关键词：Hilbert function ; Associated graded rings ; Cohen&ndash ; Macaulay ; Hilbert coefficients ; j-Multiplicity ; Residual intersections
• 刊名：Journal of Algebra
• 出版年：2013
• 出版时间：1 April, 2013
• 年：2013
• 卷：379
• 期：Complete
• 页码：31-49
• 全文大小：301 K

文摘

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 conditions, the associated graded module 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 Vaz Pinto.