Fundamental groups of links of isolated singularities

Michael Kapovich, János Kollár

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9 Scopus citations

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

Original languageEnglish (US)
Pages (from-to)929-952
Number of pages24
JournalJournal of the American Mathematical Society
Volume27
Issue number4
DOIs
StatePublished - Oct 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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