Hilbert coefficients and sequentially Cohen-Macaulay modules

TL;DR

This paper characterizes sequentially Cohen-Macaulay modules using Hilbert coefficients and arithmetic degrees, providing new insights and proofs related to Vasconcelos Vanishing Conjecture and bounds on Hilbert coefficients.

Contribution

It offers a novel characterization of sequentially Cohen-Macaulay modules via Hilbert coefficients involving arithmetic degrees, and derives new proofs and bounds.

Findings

Characterization of sequentially Cohen-Macaulay modules using Hilbert coefficients

Short proof of Vasconcelos Vanishing Conjecture for modules

Upper bound established for the first Hilbert coefficient

Abstract

The purpose of this paper is to present a characterization of sequentially Cohen-Macaulay modules in terms of its Hilbert coefficients with respect to distinguished parameter ideals. The formulas involve arithmetic degrees. Among corollaries of the main result we obtain a short proof of Vasconcelos Vanishing Conjecture for modules and an upper bound for the first Hilbert coefficient.