Designer ideals with high Castelnuovo-Mumford regularity

TL;DR

This paper presents a geometric method to construct ideals with high Castelnuovo-Mumford regularity relative to their generating degree, allowing the regularity to appear late in the resolution.

Contribution

It introduces a simple geometric construction of ideals with large regularity that can be revealed arbitrarily late in their resolutions.

Findings

Constructed ideals with high Castelnuovo-Mumford regularity

Regularity can be made to appear late in the resolution

Provides a geometric approach to understanding regularity

Abstract

The purpose of this paper is to give a simple geometric construction of ideals whose Castelnuovo-Mumford regularity is large compared to the generating degree. Moreover, our ideals have the property that the Castelnuovo-Mumford regularity is revealed as late in the resolution as desired.