Given a non-singular holomorphic foliation on a compact manifold we analyze the relationship between the versal spaces and 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 isomorphic to where is smooth and : is the forgetful map. The map is shown to be an epimorphism in two situations: (i) if , where is the sheaf of...
This paper is a continuation of Part I of the same title which has appeared at the last issue of this journal.
Let F be a transversely holomorphic foliation on a compact manifold. We show the existence of a versal space for those deformations of F which keep fixed its differentiable type if F is Hermitian or if F has complex codimension one and admits a transverse projectable connection. We also prove the existence of a versal space of deformations for the complex structures on a Lie group invariant by a cocompact subgroup.
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...
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