Some Remarks on Ideals with large Regularity and Regularity Jumps

TL;DR

This paper explores new examples of homogeneous ideals in polynomial rings with large Castelnuovo-Mumford regularity and investigates the phenomenon of regularity jumps at specific powers, contributing to understanding their behavior.

Contribution

It introduces new examples of ideals with large regularity and provides an infinite family exhibiting regularity jumps at certain powers, advancing the study of regularity behavior.

Findings

Examples of ideals with large regularity compared to generators.

Infinite family of ideals with regularity jumps at specific powers.

Insights into the behavior of Castelnuovo-Mumford regularity.

Abstract

This paper exhibits some new examples of the behavior of the Castelnuovo-Mumford regularity of homogeneous ideals in polynomial rings. More precisely, we present new examples of homogenous ideals with large regularity compared to the generating degree. Then we consider the regularity jumps of ideals. In particular we provide an infinite family of ideals having regularity jumps at a certain power.