Normally torsion-free lexsegment ideals

TL;DR

This paper characterizes all lexsegment ideals that are normally torsion-free, linking this property to the ends of the lexsegment and the constancy of the depth function.

Contribution

It provides a complete characterization of normally torsion-free lexsegment ideals based on the ends of the lexsegment and relates this to the depth function.

Findings

Characterization of normally torsion-free lexsegment ideals.

Equivalence between being normally torsion-free and constant depth function.

Insight into the structure of lexsegment ideals.

Abstract

In this paper we characterize all the lexsegment ideals which are normally torsion-free. Our characterization is given in terms of the ends of the lexsegment. We also prove that the property of being normally torsion-free is equivalent to the property of the depth function of being constant.