Foliations on the complex projective plane with many parabolic leaves
Annales de l'Institut Fourier, Tome 44 (1994) no. 4, p. 1237-1242
On démontre qu’un feuilletage sur CP 2 avec singularités hyperboliques et ayant “beaucoup" de feuilles paraboliques (i.e. sans fonctions de Green) est en fait un feuilletage linéaire. La preuve est faite en deux temps : d’abord on montre l’existence d’une feuille algébrique, en utilisant la notion de mesure harmonique, puis on montre que l’holonomie de cette feuille est linéarisable, ce qui implique aisément le résultat final.
We prove that a foliation on CP 2 with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.
@article{AIF_1994__44_4_1237_0,
     author = {Brunella, Marco},
     title = {Foliations on the complex projective plane with many parabolic leaves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {44},
     number = {4},
     year = {1994},
     pages = {1237-1242},
     doi = {10.5802/aif.1432},
     zbl = {0811.32023},
     mrnumber = {95k:32032},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1994__44_4_1237_0}
}
Brunella, Marco. Foliations on the complex projective plane with many parabolic leaves. Annales de l'Institut Fourier, Tome 44 (1994) no. 4, pp. 1237-1242. doi : 10.5802/aif.1432. http://www.numdam.org/item/AIF_1994__44_4_1237_0/

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