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Polyhedral complexes and topology of projective varieties

4:00 pm Thursday, April 5, 2011
Misha Kapovich (UC Davis)

Polyhedral complexes are obtained by gluing convex polytopes (say, Euclidean or hyperbolic) via isometric maps. In the talk I will explain how to use such complexes to construct irreducible complex-projective varieties with controlled singularities (normal crossings and Whitney umbrellas) and with prescribed fundamental groups. Polyhedral complexes that appear in the construction come from geometric topology of 1960s and 3-dimensional hyperbolic geometry (Dirichlet fundamental domains of some discrete isometry groups of hyperbolic 3-space). This is partly a joint work with Janos Kollar.

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