Powers of lexsegment ideals with linear resolution

TL;DR

This paper investigates powers of lexsegment ideals with linear resolutions, showing they maintain linear quotients and often have Koszul Rees algebras, and identifies other classes with similar properties.

Contribution

It proves that all powers of certain lexsegment ideals with linear resolutions have linear quotients and identifies classes with Koszul Rees algebras.

Findings

All powers of these lexsegment ideals have linear quotients.

The Rees algebra of a large subclass is quadratic and Koszul.

Other classes of monomial ideals with similar properties are identified.

Abstract

All powers of lexsegment ideals with linear resolution (equivalently, with linear quotients) have linear quotients with respect to suitable orders of the minimal monomial generators. For a large subclass of the lexsegment ideals the corresponding Rees algebra has a quadratic Gr\"obner basis, thus it is Koszul. We also find other classes of monomial ideals with linear quotients whose powers have linear quotients too.