  Let $X$ 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
describing 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".
