Deformations of branched Lefschetz pencils. (English) Zbl 0843.58001

It is shown that in every projective manifold \(M\) of dimension \(>3\) and \(H^1 (M, C)= 0\) any deformation of a codimension one singular foliation \({\mathcal F}\) arising from the fibers of a generic meromorphic map of the form \(f^p/ g^q\), \(p,q>0\) has a meromorphic first integral of the same type.


58A17 Pfaffian systems
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