Displaying similar documents to “On vector fields in C3 without a separatrix.”

On algebraic sets invariant by one-dimensional foliations on 𝐂 P ( 3 )

Marcio G. Soares (1993)

Annales de l'institut Fourier

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We consider the problem of extending the result of J.-P. Jouanolou on the density of singular holomorphic foliations on C P ( 2 ) without algebraic solutions to the case of foliations by curves on C P ( 3 ) . We give an example of a foliation on C P ( 3 ) with no invariant algebraic set (curve or surface) and prove that a dense set of foliations admits no invariant algebraic set.

A KAM phenomenon for singular holomorphic vector fields

Laurent Stolovitch (2005)

Publications Mathématiques de l'IHÉS

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Let X be a germ of holomorphic vector field at the origin of and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are...

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.