Displaying similar documents to “On algebraic sets invariant by one-dimensional foliations on 𝐂 P ( 3 ) ”

On vector fields in C without a separatrix.

J. Olivares-Vázquez (1992)

Revista Matemática de la Universidad Complutense de Madrid

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A family of germs at 0 of holomorphic vector fields in C without separatrices is constructed, with the aid of the blown-up foliation F in the blown-up manifold C. We impose conditions on the multiplicity and the linear part of F at its singular points (i.e., non-semisimplicity and certain nonresonancy), which are sufficient for the original vector field to be separatrix-free.

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.

Unfoldings of foliations with multiform first integrals

Tatsuo Suwa (1983)

Annales de l'institut Fourier

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Let F = ( ω ) be a codim 1 local foliation generated by a germ ω of the form ω = f 1 ... f p ∑ i = 1 p λ i d f i f i for some complex numbers λ i and germs f i of holomorphic functions at the origin in C n . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of F . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for F is equivalent to the unfolding theory for the multiform...

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.