On the volumes of complex hyperbolic manifolds with cusps

2004/07/18 by Jun-Muk Hwang, Hwang, Jun-Muk
Mathematics · #32Q45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AG #math.GT #msc:32Q45

paper · pdf · doi:10.48550/arxiv.math/0407310

to appear in International Journal of Mathematics

arxiv created 2004/07/18 · openalex publication_date 2004/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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