Higher codimensional foliations with Kupka singularities

We consider holomorphic foliations of dimension k > 1 and codimension ≥ 1 in the projective space ℙn, with a compact connected component of the Kupka set. We prove that if the transversal type is linear with positive integer eigenvalues, then the foliation consists of the fibers of a rational fibration Φ : ℙn −−→ ℙn−k. As a corollary, if dim(ℱ) ≥cod(ℱ) + 2 and has a transversal type diagonal with different eigenvalues, then the Kupka component K is a complete intersection and the leaves of the foliation define a rational fibration. The same conclusion holds if the Kupka set has a radial transversal type. Finally, as an application, we find a normal form for non-integrable codimension-one distributions on ℙn.