Holomorphic foliations in certain holomorphically convex domains of
Marco Brunella, Paulo Sad (1995)
Bulletin de la Société Mathématique de France
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Marco Brunella, Paulo Sad (1995)
Bulletin de la Société Mathématique de France
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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...
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.
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.
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...
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. Milani, C. Rea (1972)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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