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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Fundamental groups of links of isolated singularities
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by Michael Kapovich and János Kollár PDF
J. Amer. Math. Soc. 27 (2014), 929-952 Request permission

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 ${\mathbb Q}$-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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Additional Information
  • Michael Kapovich
  • Affiliation: Department of Mathematics, University of California, Davis, California 95616
  • MR Author ID: 98110
  • Email: kapovich@math.ucdavis.edu
  • János Kollár
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
  • MR Author ID: 104280
  • Email: kollar@math.princeton.edu
  • Received by editor(s): January 9, 2012
  • Received by editor(s) in revised form: September 19, 2012, February 19, 2013, and February 20, 2013
  • Published electronically: May 22, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 27 (2014), 929-952
  • MSC (2010): Primary 14B05, 14J17, 14F35; Secondary 20F05, 53C55
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00807-9
  • MathSciNet review: 3230815