Fundamental groups of links of isolated singularities

We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group G G there is a complex projective surface S S with simple normal crossing singularities only, so that the fundamental group of S S is isomorphic to G G. We use this to construct 3-dimensional isolated complex singularities so that the fundamental group of the link is isomorphic to G G. Lastly, we prove that a finitely-presented group G G is Q Q -superperfect (has vanishing rational homology in dimensions 1 and 2) if and only if G G is isomorphic to the fundamental group of the link of a rational 6-dimensional complex singularity.