Displaying similar documents to “Uniformization of the leaves of a rational vector field”

On transcendental automorphisms of algebraic foliations

B. Scárdua (2003)

Fundamenta Mathematicae

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We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation...

Codimension one foliations on complex tori

Marco Brunella (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.

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.

Foliations on the complex projective plane with many parabolic leaves

Marco Brunella (1994)

Annales de l'institut Fourier

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We prove that a foliation on C P 2 with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.

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 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...