Foliations transversely product along some component of the singular set

Abstract: In this talk we intend to give an idea of the proof that a codimension one foliation on Pn , n > 3, that is a local product near every point of some codi-mension two irreducible component of the singular set has a rational first integral. This result is a kind of generalization of a result of Calvo Andrade and M. Brunella about foliations with a Kupka component.