Linearly presented modules and bounds on the Castelnuovo-Mumford regularity of ideals

TL;DR

This paper introduces new upper bounds on the Castelnuovo-Mumford regularity of ideals by analyzing modules with linear relations, providing recursive bounds applicable in any dimension.

Contribution

It develops a novel approach to estimate regularity using modules generated in degree zero with linear relations, leading to improved bounds across dimensions.

Findings

New upper bounds for regularity in dimension one.

Recursive techniques for bounds in higher dimensions.

Enhanced understanding of modules with linear relations.

Abstract

We estimate the Castelnuovo-Mumford regularity of ideals in a polynomial ring over a field by studying the regularity of certain modules generated in degree zero and with linear relations. In dimension one, this process gives a new type of upper bounds. By means of recursive techniques this also produces new upper bounds for ideals in any dimension.