On algebraic sets invariant by one-dimensional foliations on 𝐂P(3)
Soares, Marcio G.
Annales de l'Institut Fourier, Tome 43 (1993), p. 143-162 / Harvested from Numdam
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On considère le problème d’étendre le résultat de J.-P. Jouanolou à la densité des feuilletages holomorphes singuliers dans CP(2), sans solution algébrique, au cas des feuilletages par des courbes dans CP(3). On donne un exemple de feuilletage dans CP(3) sans ensemble algébrique invariant (courbe ou surface) et on montre qu’un ensemble dense de feuilletages n’admet pas d’ensemble algébrique invariant.

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.

@article{AIF_1993__43_1_143_0,
     author = {Soares, Marcio G.},
     title = {On algebraic sets invariant by one-dimensional foliations on ${\bf C}P(3)$},
     journal = {Annales de l'Institut Fourier},
     volume = {43},
     year = {1993},
     pages = {143-162},
     doi = {10.5802/aif.1325},
     mrnumber = {94b:32057},
     zbl = {0770.57016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1993__43_1_143_0}
}

Soares, Marcio G. On algebraic sets invariant by one-dimensional foliations on ${\bf C}P(3)$. Annales de l'Institut Fourier, Tome 43 (1993) pp. 143-162. doi : 10.5802/aif.1325. http://gdmltest.u-ga.fr/item/AIF_1993__43_1_143_0/

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