Logarithmic bundles and Line arrangements, an approach via the standard construction

TL;DR

This paper introduces a new approach to studying logarithmic sheaves linked to hyperplane arrangements using projective duality and vector bundle techniques, with a focus on arrangements with high multiplicity points.

Contribution

It presents a novel method combining projective duality and vector bundle theory to analyze the freeness of line arrangements, especially those with high multiplicity points.

Findings

New framework for logarithmic sheaves analysis

Characterization of freeness in high multiplicity arrangements

Application of duality and vector bundles in arrangement theory

Abstract

We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line arrangements having a point with high multiplicity.