Castelnuovo-Mumford regularity of the associated graded module in dimension one

TL;DR

This paper establishes an upper bound for the Castelnuovo-Mumford regularity of the associated graded module of a one-dimensional module using Hilbert coefficients and explores conditions for the bound to be tight.

Contribution

It provides a new upper bound for regularity in terms of Hilbert coefficients and characterizes when this bound is achieved.

Findings

Upper bound for regularity in terms of Hilbert coefficients

Conditions under which the bound is attained

Insights into the structure of associated graded modules in dimension one

Abstract

An upper bound for the Castelnuovo-Mumford regularity of the associated graded module of an one-dimension module is given in term of its Hilbert coeffcients. It is also investigated when the bound is attained.