Arturo Fernández-Pérez (2011)
Annales de la faculté des sciences de Toulouse Mathématiques
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We investigate real analytic Levi-flat hypersurfaces tangent to holomorphic webs. We introduce the notion of first integrals for local webs. In particular, we prove that a -web with finitely many invariant subvarieties through the origin tangent to a Levi-flat hypersurface has a holomorphic first integral.
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...
Marco Brunella (1997)
Publicacions Matemàtiques
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One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation. ...
Maria Lucia Fania, Andrew John Sommese (1988)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Paulo Sad (1997)
Annales de l'institut Fourier
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We consider the problem of realization of a linear subgroup of as the linear holonomy group of an algebraic curve which is a leaf of a foliation of .
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 .