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

Abstract

Let X⊂ C P N 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 C P N . 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.