Regularity of Koszul modules

TL;DR

This paper establishes upper bounds on the regularity of Koszul homology modules for various classes of ideals and modules over polynomial rings, advancing understanding of their algebraic complexity.

Contribution

It provides new upper bounds on the regularity of Koszul homology modules for specific classes of ideals and modules in polynomial rings.

Findings

Upper bounds on regularity for certain classes of ideals.

Results applicable to a range of graded modules.

Enhanced understanding of Koszul homology regularity.

Abstract

Let $K$ be a field and let $S = K[X_1, \ldots, X_n]$. Let $I$ be a graded ideal in $S$ and let $M$ be a finitely generated graded $S$-module. We give upper bounds on the regularity of Koszul homology modules $H_i(I, M)$ for several classes of $I$ and $M$.