On Hilbert coefficients and sequentially generalized Cohen-Macaulay modules

TL;DR

This paper characterizes sequentially generalized Cohen-Macaulay modules over certain rings using bounds on differences between Hilbert coefficients and arithmetic degrees for distinguished parameter ideals.

Contribution

It establishes a new equivalence condition for sequentially generalized Cohen-Macaulay modules based on Hilbert coefficients and arithmetic degrees.

Findings

Bounded differences characterize sequentially generalized Cohen-Macaulay modules.

Provides a new criterion involving Hilbert coefficients and arithmetic degrees.

Applicable to modules over homomorphic images of Cohen-Macaulay rings.

Abstract

This paper shows that if $R$ is a homomorphic image of a Cohen-Macaulay local ring, then $R$-module $M$ is sequentially generalized Cohen-Macaulay if and only if the difference between Hilbert coefficients and arithmetic degrees for all distinguished parameter ideals of $M$ are bounded.