Abstract
In this paper, we show that the canonical divisor of a smooth toroidal compactification of a complex hyperbolic manifold must be nef if the dimension is greater or equal to three. Moreover, if n ≥ 3 we show that the numerical dimension of the canonical divisor of a smooth n-dimensional compactification is always bigger or equal to n - 1. We also show that up to a finite étale cover all such compactifications have ample canonical class, therefore refining a classical theorem of Mumford and Tai. Finally, we improve in all dimensions n ≥ 3 the cusp count for finite volume complex hyperbolic manifolds given in [DD15a].
Original language | English (US) |
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Pages (from-to) | 1005-1022 |
Number of pages | 18 |
Journal | Mathematical Research Letters |
Volume | 24 |
Issue number | 4 |
DOIs | |
State | Published - 2017 |
All Science Journal Classification (ASJC) codes
- General Mathematics