On the volumes of complex hyperbolic manifolds with cusps

Details On the volumes of complex hyperbolic manifolds with cusps On the volumes of complex hyperbolic manifolds with cusps

2004-07-18

arxiv.org/abs/math/0407310v1

Mathematics

Algebraic Geometry

to appear in International Journal of Mathematics

Scientific paper

We study the problem of bounding the number of cusps of a complex hyperbolic
manifold in terms of its volume. Applying algebro-geometric methods using
Mumford's work on toroidal compactifications and its generalization due to N.
Mok and W.-K. To, we get a bound which is considerably better than those
obtained previously by methods of geometric topology.

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