Displaying similar documents to “On Levi-flat hypersurfaces tangent to holomorphic webs”

On the smoothness of Levi-foliations.

D. E. Barrett, John Erik Fornaess (1988)

Publicacions Matemàtiques

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We study the regularity of the induced foliation of a Levi-flat hypersurface in C, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.

A note on projective Levi flats and minimal sets of algebraic foliations

Alcides Lins Neto (1999)

Annales de l'institut Fourier

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In this paper we prove that holomorphic codimension one singular foliations on ℂ ℙ n , n ≥ 3 have no non trivial minimal sets. We prove also that for n ≥ 3 , there is no real analytic Levi flat hypersurface in ℂ ℙ n .

Singular Levi-flat hypersurfaces and codimension one foliations

Marco Brunella (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.

Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations

O. Calvo-Andrade (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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It is a known fact that the space of codimension one holomorphic foliations with singularities with a given ‘normal bundle’ has a natural structure of an algebraic variety. The aim of this paper is to consider the problem of the description of its irreducible components. To do this, we are interested in the problem of the existence of an integral factor of a twisted integrable differential 1–form defined on a projective manifold. We are going to do a geometrical analysis of the codimension...

On deformations of holomorphic foliations

Joan Girbau, Marcel Nicolau (1989)

Annales de l'institut Fourier

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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 ) × 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 f ) = 0 , where Θ ℱ f is...