Frédéric Touzet : Codimension one foliation with pseudo-effective conormal bundle - lecture 1

Let X be a projective manifold equipped with a codimension 1 (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. Basic examples of such distributions are provided by the kernel of a holomorphic one form, necessarily closed when the ambient is projective. More generally, due to a theorem of Jean-Pierre Demailly, a distribution with conormal sheaf pseudoeffective is actually integrable and thus defines a codimension 1 holomorphic foliation F. In this series of lectures, we would aim at describing the structure of such a foliation, especially in the non abundant case, i.e when F cannot be defined by a holomorphic one form (even passing through a finite cover). It turns out that \F is the pull-back of one of the "canonical foliations" on a Hilbert modular variety. This result remains valid for 'logarithmic foliated pairs''.

CIRM VIRTUAL EVENT
Recorded during the research school "Geometry and Dynamics of Foliations " the May 05, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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