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On deformations of holomorphic foliations

Joan GirbauMarcel Nicolau — 1989

Annales de l'institut Fourier

Given a non-singular holomorphic foliation on a compact manifold M we analyze the relationship between the versal spaces K and K tr of deformations of as a holomorphic foliation and as a transversely holomorphic foliation respectively. With this purpose, we prove the existence of a versal unfolding of parametrized by an analytic space K f isomorphic to π - 1 ( 0 ) × Σ where Σ is smooth and π : K K tr is the forgetful map. The map π is shown to be an epimorphism in two situations: (i) if H 2 ( M , Θ f ) = 0 , where Θ f is the sheaf of...

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