Fundamental groups of links of isolated singularities

Michael Kapovich; János Kollár

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arXiv · 1109.4047

Fundamental groups of links of isolated singularities

Michael Kapovich·János Kollár

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Abstract

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 if G is isomorphic to the fundamental group of the link of a rational 6-dimensional complex singularity.

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Michael Kapovich, János Kollár. 2011-09-19. Fundamental groups of links of isolated singularities. https://arxiv.org/abs/1109.4047

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