The second Hilbert coefficient of modules with almost maximal depth

2025/06/21 by Trung, Van Duc · 1 citation
#13H10 #Commutative Algebra (math.AC) #F.2.2 #FOS: Mathematics #I.2.7

paper · doi:10.48550/arxiv.2506.17591

Abstract

Let \mathbbM = \ M_n \ be a good \mathfrakq-filtration of a finitely generated R-module M of dimension d, where (R,\mathfrakm) is a local ring and \mathfrakq is an \mathfrakm-primary ideal of R. In case depth(M) ≥ d-1, we give an upper bound for the second Hilbert coefficient e₂(\mathbbM) generalizing results by Huckaba-Marley and Rossi-Valla proved assuming that M is Cohen-Macaulay. We also give a condition for the equality, which relates to the depth of the associated graded module gr_\mathbbM(M). A lower bound on e₂(\mathbbM) is proved generalizing a result by Rees and Narita.

Citations

• Hilbert Coefficients of Parameter Ideals
• On the Chern number of a filtration
• Hilbert Functions of Filtered Modules
• Ratliff-Rush Filtrations associated with ideals and modules over a Noetherian ring

Cited by

• Bounds on the second Hilbert coefficient and the depth of the associated graded ring

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