Displaying similar documents to “Stability of foliations induced by rational maps”

The polar curve of a foliation on ℙ 2

Rogério S. Mol (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We study some properties of the polar curve P l ℱ associated to a singular holomorphic foliation ℱ on the complex projective plane ℙ 2 . We prove that, for a generic center l ∈ ℙ 2 , the curve P l ℱ is irreducible and its singular points are exactly the singular points of ℱ with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of ℱ and for its number of radial singularities.

Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations

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...

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.

Chern numbers of a Kupka component

Omegar Calvo-Andrade, Marcio G. Soares (1994)

Annales de l'institut Fourier

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We will consider codimension one holomorphic foliations represented by sections ω ∈ H 0 ( ℙ n , Ω 1 ( k ) ) , and having a compact Kupka component K . We show that the Chern classes of the tangent bundle of K behave like Chern classes of a complete intersection 0 and, as a corollary we prove that K is a complete intersection in some cases.