On codimension 1 families of singular meromorphic foliations having a meromorphic first integral

Let X⊂CPN be a smooth compact complex manifold. Here we study certain codimension 1 holomorphic foliations with singularities on X cut out by a pencil of hyperplanes through a codimension 2 linear subspace of CPN. We classify the codimension 1 strata of the closure, M, of the foliations on X induced by Lefschetz pencils. Under certain cohomological assumptions we describe M. For certain X we study also a few related holomorphic singular foliations of higher codimension.