Hilbert coefficients and partial Euler–Poincaré characteristics of Koszul complexes of d-sequences

Abstract

We construct in a finitely generated module over a Cohen–Macaulay local ring several subquotient modules. In terms of multiplicities of these subquotients, we give precise formulas computing all the partial Euler–Poincaré characteristics of the Koszul complex and the Hilbert coefficients of the module relative to an almost p-standard system of parameters – a very strict subclass of d-sequences on the module. The formulas enable us to establish some comparison between the partial Euler–Poincaré characteristics and the Hilbert coefficients.