Dihedral coverings of algebraic surfaces and their application

In this article, we study dihedral coverings of algebraic surfaces branched along curves with at most simple singularities. A criterion for a reduced curve to be the branch locus of some dihedral covering is given. As an application we have the following:

Let $B$ be a reduced plane curve of even degree $d$ having only $a$ nodes and $b$ cusps. If $2a + 6b > 2d^2 - 6d + 6$, then $\pi_1(\mathbf{P}^2 \setminus B)$ is non-abelian.

Note that Nori's result implies that $\pi_1(\mathbf{P}^2 \setminus B)$ is abelian, provided that $2a + 6b < d^2$.