Supersolvable resolutions of line arrangements

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 ${\mathbb{P}}_{\mathbb{C}}^2$ and we show that these numbers $\mathbf{\text{are}}\mathbf{\text{not}}$ determined by the intersection lattice of the given arrangement.