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Inventiones mathematicae

, Volume 194, Issue 3, pp 631–672 | Cite as

Dirichlet fundamental domains and topology of projective varieties

  • Michael Kapovich
Article

Abstract

We prove that for every finitely-presented group G there exists a 2-dimensional irreducible complex-projective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas.

Keywords

Projective Variety Fundamental Domain Normal Crossing Polyhedral Complex Cartan Involution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This paper grew out of our work [17] with János Kollár and I am grateful to him for questions, comments and suggestions. In particular, he explained to me that Whitney umbrella singularities appear as ℤ2-quotients of normal crossings and suggested the dimension reduction from 3 to 2. I am grateful to Akira Ushijima for sharing with me [24]. I am also grateful to the referee for useful remarks and suggestions. Partial financial support for this work was provided by the NSF grants DMS-09-05802 and DMS-12-05312.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

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