Effective results for complex hyperbolic manifolds
Differential Geometry
2015-06-12 v5 Algebraic Geometry
Geometric Topology
Abstract
The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef canonical divisor. We derive effective very ampleness results for toroidal compactifications of finite volume complex hyperbolic manifolds. We estimate the number of ends of such manifolds in terms of their volume. We give effective bounds on the number of complex hyperbolic manifolds with given upper bounds on the volume. Moreover, we give two sided bounds on their Picard numbers in terms of the volume and the number of cusps.
Cite
@article{arxiv.1212.0501,
title = {Effective results for complex hyperbolic manifolds},
author = {Gabriele Di Cerbo and Luca F. Di Cerbo},
journal= {arXiv preprint arXiv:1212.0501},
year = {2015}
}
Comments
Some changes according the comments of the referee and references updated