no. 1
On algebraic sets invariant by one-dimensional foliations on 𝐂P(3)
Annales de l'Institut Fourier, Volume 43 (1993) no. 1, pp. 143-162.

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

On considĂšre le problĂšme d’étendre le rĂ©sultat de J.-P. Jouanolou Ă  la densitĂ© des feuilletages holomorphes singuliers dans CP(2), sans solution algĂ©brique, au cas des feuilletages par des courbes dans CP(3). On donne un exemple de feuilletage dans CP(3) sans ensemble algĂ©brique invariant (courbe ou surface) et on montre qu’un ensemble dense de feuilletages n’admet pas d’ensemble algĂ©brique invariant.

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     title = {On algebraic sets invariant by one-dimensional foliations on ${\bf C}P(3)$},
     journal = {Annales de l'Institut Fourier},
     pages = {143--162},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {1},
     year = {1993},
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Soares, Marcio G. On algebraic sets invariant by one-dimensional foliations on ${\bf C}P(3)$. Annales de l'Institut Fourier, Volume 43 (1993) no. 1, pp. 143-162. doi : 10.5802/aif.1325. https://aif.centre-mersenne.org/articles/10.5802/aif.1325/

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