On the topology of some quasi-projective surfaces

Abstract

Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental groups and the associated Galois coverings, the second homotopy groups and the mixed Hodge structure on the first cohomology group.Comment: version 2 contains new examples and many new references following suggestions by Ciro Ciliberto and De-Qi Zhan