Birational geometry of complex hyperbolic manifolds
-- Gabriele di Cerbo, November 6, 2015

<p>

In 1984 Hirzebruch constructed the first examples of smooth toroidal
compactifications of ball quotients with non-nef canonical divisor. In
this talk, I will show that if the dimension is greater than or equal to
three, then such examples cannot exist. We will use this result to
reprove and improve classical theorems, such as boundedness of
hyperbolic manifolds, Baily-Borel embeddings and cusp counts.