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

Marcio G. Soares — 1993

Annales de l'institut Fourier

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.

Chern numbers of a Kupka component

Omegar Calvo-Andrade; Marcio G. Soares — 1994

Annales de l'institut Fourier

We will consider codimension one holomorphic foliations represented by sections $ω \in H^{0} (ℙ^{n}, Ω^{1} (k))$ , 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.

Projective varieties invariant by one-dimensional foliations.

Soares, Marcio G. — 2000

Annals of Mathematics. Second Series

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

Chern numbers of a Kupka component

Projective varieties invariant by one-dimensional foliations.

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