The Dual Hilbert–Samuel Function of a Maximal Cohen-Macaulay Module

Abstract

Let R be a Cohen-Macaulay local ring with a canonical module R . Let I be an -primary ideal of R and M, a maximal Cohen-Macaulay R-module. We call the function n −→ Hom R M R /I n+1 R the dual Hilbert-Samuel function of M with respect to I. By a result of Theodorescu, this function is of polynomial type. We study its first two normalized coefficients. In particular, we analyze the case when R is Gorenstein.