On irreducible sextics with non-abelian fundamental group

Abstract

We calculate the fundamental groups $\pi = \pi_1 (\mathbb{P}^2 \smallsetminus B)$ for all irreducible plane sextics $B \subset \mathbb{P}^2$ with simple singularities for which $\pi$ is known to admit a dihedral quotient $\mathbb{D}_{10}$. All groups found are shown to be finite, two of them being of large order: 960 and 21600.