Finite volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications

2011/01/22 by Luca Fabrizio Di Cerbo, Di Cerbo, Luca Fabrizio
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.1101.4263

Some changes according the comments of the referee. Added acknowledgments

arxiv created 2012/01/14 · arxiv updated 2012/01/17

Abstract

We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are given. In particular we show that there are compact complex surfaces which admit Riemannian metrics of nonpositive curvature, but which do not admit Kähler metrics of nonpositive curvature. An infinite class of such examples arise as smooth toroidal compactifications of ball quotients.

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