Inventiones mathematicae

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

Dirichlet fundamental domains and topology of projective varieties

  • Michael Kapovich


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.


Projective Variety Fundamental Domain Normal Crossing Polyhedral Complex Cartan Involution 
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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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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

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