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.
|Original language||English (US)|
|Number of pages||16|
|Journal||Journal of the London Mathematical Society|
|State||Published - Apr 17 2015|
All Science Journal Classification (ASJC) codes