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On deformations of holomorphic foliations

Joan Girbau; Marcel Nicolau — 1989

Annales de l'institut Fourier

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

Pseudo-differential operators on V-manifolds and foliations (II).

Joan Girbau; Marcel Nicolau — 1980

Collectanea Mathematica

This paper is a continuation of Part I of the same title which has appeared at the last issue of this journal.

Pseudo-differential operators on V-manifolds and foliations (I).

Joan Girbau; Marcel Nicolau — 1979

Collectanea Mathematica

Holomorphic flows and complex structures on products of odd dimensional spheres.

Jean Jaques Loeb; Marcel Nicolau — 1996

Mathematische Annalen

Déformations des feuilletages transversalement holomorphes à type différentiable fixé.

A. El Kacimi Alaoui; Marcel 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 Amorós; Mònica Manjarín; Marcel 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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