Hypersurfaces quasi-invariant by codimension one foliations
Hypersurfaces quasi-invariant by codimension one foliations
Abstract We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem for foliations on 3-folds admitting an infinite number of extremal rays.