Stability of branched pull-back projective foliations

Original · EN

We prove that, if n≥ 3, a singular foliation F on Pⁿ which can be written as pull-back, where G is a foliation in P² of degree d≥2 with one or three invariant lines in general position and f:Pⁿ--->P², deg(f)=ν≥2, is an appropriated rational map, is stable under holomorphic deformations. As a consequence we conclude that the closure of the sets {F= f*(G)} are new irreducible components of the space of holomorphic foliations of certain degrees.