Lefschetz Properties and Hyperplane Arrangements

TL;DR

This paper extends the study of Lefschetz properties and almost revlex ideals from Artinian to non-Artinian cases and applies these results to analyze the Jacobian algebra of hyperplane arrangements.

Contribution

It generalizes known Lefschetz properties to non-Artinian cases and connects these to hyperplane arrangements through Jacobian algebra analysis.

Findings

Lefschetz properties hold in non-Artinian cases

Results applicable to Jacobian algebra of hyperplane arrangements

Extension of almost revlex ideal concepts

Abstract

In this article, we study the weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, proving that several results known in the Artinian case hold also in this more general setting. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements.