Supersolvable resolutions of line arrangements

TL;DR

This paper investigates the numerical properties of supersolvable resolutions of line arrangements in the complex projective plane, providing bounds and showing these are not solely determined by intersection lattices.

Contribution

It introduces bounds on extension to supersolvability numbers and demonstrates their independence from intersection lattice data.

Findings

Upper bounds on extension to supersolvability numbers for certain arrangements

Supersolvability extension numbers are not determined by intersection lattices

Analysis of extreme line arrangements in complex projective plane

Abstract

The main purpose of the present paper is to study the numerical properties of supersolvable resolutions of line arrangements. We provide upper-bounds on the so-called extension to supersolvability numbers for certain extreme line arrangements in $\mathbb{P}^{2}_{\mathbb{C}}$ and we show that these numbers \textbf{are not} determined by the intersection lattice of the given arrangement.