The dual Hilbert-Samuel function of a Maximal Cohen-Macaulay module

2008/09/19 by Tony J. Puthenpurakal, Puthenpurakal, Tony J., Fahed Zulfeqarr +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AC #msc:13A30 #msc:13D45

paper · pdf · doi:10.48550/arxiv.0809.3353

arxiv created 2008/09/19 · arxiv updated 2009/12/01

Abstract

Let R be a Cohen-Macaulay local ring with a canonical module ω_R. Let I be an \m-primary ideal of R and M, a maximal Cohen-Macaulay R-module. We call the function n\longmapsto ℓ (\Hom_R(M,ω_R/Iⁿ⁺¹ ω_R)) the dual Hilbert-Samuel function of M with respect to I. By a result of Theodorescu this function is a polynomial function. We study its first two normalized coefficients.

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