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Let $X$ a projective manifold equipped with a codimension $1$ (maybesingular) distribution whose conormal sheaf is assumed to be pseudoeffective.By a theorem of Jean-Pierre Demailly, this distribution is actually integrableand thus defines a codimension $1$ holomorphic foliation $\F$. We aim atdescribing the structure of such a foliation, especially in the non abundantcase: It turns out that $\F$ is the pull-back of one of the "canonicalfoliations" on a Hilbert modular variety. This result remains valid for"logarithmic foliated pairs".

On the structure of codimension 1 foliations with pseudoeffective conormal bundle