1,554 research outputs found
On the canonical divisor of smooth toroidal compactifications
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 we show that the numerical
dimension of the canonical divisor of a smooth -dimensional compactification
is always bigger or equal to . We also show that up to a finite \'etale
cover all such compactifications have ample canonical class, therefore refining
a classical theorem of Mumford and Tai. Finally, we improve in all dimensions
the cusp count for finite volume complex hyperbolic manifolds given
in [DD15a].Comment: Title shortened to match published versio
On Fujita's log spectrum conjecture
We prove Fujita's log spectrum conjecture. It follows from the ACC of a
suitable set of pseudo-effective thresholds.Comment: Corollary 3.4 improved and fixed some typo
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