Singular sets of holonomy maps for algebraic foliations

Gabriel Calsamiglia; Bertrand Deroin; Sidney Frankel; Adolfo Guillot

Displaying similar documents to “Singular sets of holonomy maps for algebraic foliations”

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...

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.

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 $ℂ ℙ^{n}, n \geq 3$ have no non trivial minimal sets. We prove also that for $n \geq 3$ , there is no real analytic Levi flat hypersurface in $ℂ ℙ^{n}$ .

A Theorem of Versality for Unfoldings of Complex Analytic Foliation Singularities.

Tatsuo Suwa (1981/82)

Inventiones mathematicae

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On topological rigidity of projective foliations

A. Lins Neto, P. Sad, B. Scárdua (1998)

Bulletin de la Société Mathématique de France

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Integrals for holomorphic foliations with singularities having all leaves compact

Xavier Gomez-Mont (1989)

Annales de l'institut Fourier

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We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.

Existence of foliations on 4-manifolds.

Scorpan, Alexandru (2003)

Algebraic & Geometric Topology

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Holomorphic foliations in certain holomorphically convex domains of $ℂ^{2}$

Marco Brunella, Paulo Sad (1995)

Bulletin de la Société Mathématique de France

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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.