Holomorphic foliations in certain holomorphically convex domains of
Marco Brunella, Paulo Sad (1995)
Bulletin de la Société Mathématique de France
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Displaying similar documents to “On topological rigidity of projective foliations”
Holomorphic foliations in certain holomorphically convex domains of
Singular sets of holonomy maps for algebraic foliations
Gabriel Calsamiglia, Bertrand Deroin, Sidney Frankel, Adolfo Guillot (2013)
Journal of the European Mathematical Society
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In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty...
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 have no non trivial minimal sets. We prove also that for , there is no real analytic Levi flat hypersurface in .
On the real secondary classes of transversely holomorphic foliations
Taro Asuke (2000)
Annales de l'institut Fourier
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In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space of the real secondary classes to the space of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation....
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...
Unfoldings of holomorphic foliations.
Xavier Gómez-Mont (1989)
Publicacions Matemàtiques
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The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.
Uniformization of the leaves of a rational vector field
Alberto Candel, X. Gómez-Mont (1995)
Annales de l'institut Fourier
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We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.