Displaying similar documents to “Reduction of the singularities of foliations and applications”

On dicritical foliations and Halphen pencils

Luís Gustavo Mendes, Paulo Sad (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.

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.

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 stability theorem for foliations with singularities

Andrzej Piątkowski

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CONTENTSIntroduction...........................................................................................51. Preliminaries.....................................................................................62. Chains along a curve......................................................................143. Some topological properties of foliations with singularities..............224. Holonomy group of a leaf................................................................235. A stability...

Holomorphic foliations by curves on ℙ 3 with non-isolated singularities

Gilcione Nonato Costa (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let ℱ be a holomorphic foliation by curves on ℙ 3 . We treat the case where the set Sing ( ℱ ) consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of ℱ , the multiplicity of ℱ along the curves and the degree and genus of the curves.