Generators of Koszul homology with coefficients in a $\underline{g}$-weak complete intersection module

TL;DR

This paper introduces a new class of modules called g-weak complete intersection modules, providing explicit formulas for their Koszul homology generators and exploring their relationship with existing weak complete intersection ideals.

Contribution

It defines g-weak complete intersection modules, derives explicit formulas for their Koszul homology generators, and connects these modules to previously studied weak complete intersection ideals.

Findings

Explicit formulas for Koszul homology generators with g-weak complete intersection coefficients

Generalization of previous work on weak complete intersection ideals

Establishment of connections between g-weak and weak complete intersection ideals

Abstract

We discuss a class of modules, which we call $\underline{g}$-weak complete intersection modules, inspired by the weak complete intersection ideals studied by Rahmati, Striuli, and Yang and we present explicit formulas for the generators of Koszul homology with coefficients in a $\underline{g}$-weak complete intersection module. This generalizes work of Herzog and of Corso, Goto, Huneke, Polini, and Ulrich. We use these explicit formulas to study connections between $\underline{g}$-weak complete intersection ideals and weak complete intersection ideals.