Deformations of branched Lefschetz Pencils

LetM be a projective manifold of dimension 3 andH ¹ (M, )=0. We will show that a deformation of a codimension one singular foliation arising from the fibers of a generic meromorphic map of the formf ^p /g ^q ,p, q>0 has a meromorphic first integral of the same type.Supported by Conacyt: 3398 E9307.     

Foliations with a Kupka component on algebraic manifolds

We consider codimension one holomorphic foliations in complex projective manifolds of dimension at least 3, having a compact Kupka component and represented by integrable holomorphic sections of the bundleTM ^*L, whereL denotes a very ample holomorphic line bundle. We will show that, if the transversal type is not the radial vector field andH ¹ (M,) = 0, then the foliation has a meromorphic first integral.Supported by Conacyt: 3398-E 9307