ON THE STRUCTURE OF CODIMENSION 1 FOLIATIONS WITH PSEUDOEFFECTIVE CONORMAL BUNDLE.

Abstract. LetX a projective manifold equipped with a codimension 1 (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean-Pierre Demailly, this distribution is actually integrable and thus defines a codimension 1 holomorphic foliation F. We aim at de-scribing the structure of such a foliation, especially in the non abundant case: 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”