Geometry/topology Seminar
Tuesday, March 24, 2009, 4:30pm, 119 Physics
Julio Rebelo (Institut de Mathématiques de Toulouse)
On closed currents invariant by holomorphic foliations
Abstract:- Let M be an algebraic complex surface equipped with a
singular foliation F. We assume that F leaves invariant a closed current on M or, equivalently, that F possesses a transversely invariant measure. The purpose of this talk is two-fold. First we want to classify
the pairs (M, F) as above, a problem that is usually
regarded as a step towards developing a suitable Ergodic Theory
for these foliations. On the other hand we want to explain the
connection of this problem with the Kobayashi hyperbolicity of
general type surfaces. In particular we shall sketch a new proof
of McQuillan's theorem proving the Green-Griffiths conjecture
for general type surfaces having positive Segre class. [video]
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