We consider the problem of extending the result of J.-P. Jouanolou on the density of singular holomorphic foliations on without algebraic solutions to the case of foliations by curves on . We give an example of a foliation on 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 dâĂ©tendre le rĂ©sultat de J.-P. Jouanolou Ă la densitĂ© des feuilletages holomorphes singuliers dans , sans solution algĂ©brique, au cas des feuilletages par des courbes dans . On donne un exemple de feuilletage dans sans ensemble algĂ©brique invariant (courbe ou surface) et on montre quâun ensemble dense de feuilletages nâadmet pas dâensemble algĂ©brique invariant.
@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}, pages = {143--162}, publisher = {Imprimerie Louis-Jean}, address = {Gap}, volume = {43}, number = {1}, year = {1993}, doi = {10.5802/aif.1325}, mrnumber = {94b:32057}, zbl = {0770.57016}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1325/} }
TY - JOUR TI - On algebraic sets invariant by one-dimensional foliations on ${\bf C}P(3)$ JO - Annales de l'Institut Fourier PY - 1993 DA - 1993/// SP - 143 EP - 162 VL - 43 IS - 1 PB - Imprimerie Louis-Jean PP - Gap UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1325/ UR - https://www.ams.org/mathscinet-getitem?mr=94b:32057 UR - https://zbmath.org/?q=an%3A0770.57016 UR - https://doi.org/10.5802/aif.1325 DO - 10.5802/aif.1325 LA - en ID - AIF_1993__43_1_143_0 ER -
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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