The asphericity conjecture for complements of PK arrangements

Let an arrangement be a collection of weighted lines in $\mathbb{CP}^2$ satisfying the conditions of Theorem existence. Its complement is the space obtained by removing the arrangement's lines from $\mathbb{CP}^2$. The asphericity conjecture for complements of PK arrangements. For every arrangement satisfying the conditions of Theorem existence, its complement is of type $K(\pi,1)$. This would assert that the complement is aspherical, so its homotopy type is determined by its fundamental group.