New characterizations of freeness for hyperplane arrangements

TL;DR

This paper introduces two novel characterizations of freeness in hyperplane arrangements using the generic initial ideal and sectional matrix of the Jacobian ideal, advancing the algebraic understanding of these structures.

Contribution

It provides new algebraic criteria for freeness in hyperplane arrangements based on the study of the generic initial ideal and sectional matrix.

Findings

New criteria for freeness using algebraic invariants

Enhanced understanding of the Jacobian ideal in arrangements

Potential applications to classification of arrangements

Abstract

In this article we describe two new characterizations of freeness for hyperplane arrangements via the study of the generic initial ideal and of the sectional matrix of the Jacobian ideal of arrangements.