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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 ∈ 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.

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