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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...

Déformations des feuilletages transversalement holomorphes à type différentiable fixé.

A. El Kacimi AlaouiMarcel Nicolau — 1989

Publicacions Matemàtiques

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.

Deformations of Kähler manifolds with nonvanishing holomorphic vector fields

Jaume AmorósMònica ManjarínMarcel Nicolau — 2012

Journal of the European Mathematical Society

We study compact Kähler manifolds X 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 𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛𝑠 , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of X . We extend Calabi’s theorem on the structure of compact Kähler...

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