THE DUAL HILBERT-SAMUEL FUNCTION OF A MAXIMAL COHEN-MACAULAY MODULE

摘要

Let R be a Cohen-Macaulay local ring with a canonical module omega(R). Let I be an m-primary ideal of R and M, a maximal Cohen-Macaulay R-module. We call the function n -> l (Hom(R) (M, omega(R)/In+1 omega(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.