Numerical invariants and moduli spaces for line arrangements

TL;DR

This paper investigates the classification of line arrangements in the complex projective plane using numerical invariants and introduces a new way to characterize free plane curves through algebraic regularity measures.

Contribution

It provides a novel partition of line arrangement spaces based on intersection lattice types and offers a new characterization of free plane curves via Castelnuovo-Mumford regularity.

Findings

Partition of line arrangements by intersection lattice types

New characterization of free plane curves using algebraic regularity

Insights into the structure of Milnor/Jacobian algebras

Abstract

Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane curves using the Castelnuovo-Mumford regularity of the associated Milnor/Jacobian algebra.