Department of Mathematics

© 2014 American Mathematical Society. All rights reserved. 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 there is a complex projective surface S with simple normal crossing singularities only, so that the fundamental group of S is isomorphic to G. We use this to construct 3-dimensional isolated complex singularities so that the fundamental group of the link is isomorphic to G. Lastly, we prove that a finitely- presented group G is Q-superperfect (has vanishing rational homology in dimensions 1 and 2) if and only G if is isomorphic to the fundamental group of the link of a rational 6-dimensional complex singularity.