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

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

2011-01-22

arxiv.org/abs/1101.4263v2

Mathematics

Differential Geometry

Some changes according the comments of the referee. Added acknowledgments

Scientific paper

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 K\"ahler metrics of nonpositive curvature. An infinite class of such examples arise as smooth toroidal compactifications of ball quotients.

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