Finite volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications
Differential Geometry
2012-01-17 v2 Algebraic Geometry
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 K\"ahler metrics of nonpositive curvature. An infinite class of such examples arise as smooth toroidal compactifications of ball quotients.
Cite
@article{arxiv.1101.4263,
title = {Finite volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications},
author = {Luca Fabrizio Di Cerbo},
journal= {arXiv preprint arXiv:1101.4263},
year = {2012}
}
Comments
Some changes according the comments of the referee. Added acknowledgments