The supersolvable arrangement double-point conjecture

Let ${\mathbb K}={\mathbb C}$, and let ${\mathcal A}$ be a supersolvable projective line arrangement. Write $n_2({\mathcal A})$ for the number of its double points.

Supersolvable arrangement double-point conjecture. One has

$$n_2({\mathcal A}) \ge \frac{|{\mathcal A}|}{2}.$$

This is the complex supersolvable version of the Dirac–Motzkin conjecture. The corresponding real statement is known, and the displayed inequality is implied by the theorem proved later in the paper; its historical status as a conjecture is therefore resolved.