We prove that a foliation on 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.
On démontre qu’un feuilletage sur 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.
@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}, pages = {1237--1242}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {44}, number = {4}, year = {1994}, doi = {10.5802/aif.1432}, zbl = {0811.32023}, mrnumber = {95k:32032}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1432/} }
TY - JOUR AU - Brunella, Marco TI - Foliations on the complex projective plane with many parabolic leaves JO - Annales de l'Institut Fourier PY - 1994 SP - 1237 EP - 1242 VL - 44 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1432/ DO - 10.5802/aif.1432 LA - en ID - AIF_1994__44_4_1237_0 ER -
%0 Journal Article %A Brunella, Marco %T Foliations on the complex projective plane with many parabolic leaves %J Annales de l'Institut Fourier %D 1994 %P 1237-1242 %V 44 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1432/ %R 10.5802/aif.1432 %G en %F AIF_1994__44_4_1237_0
Brunella, Marco. Foliations on the complex projective plane with many parabolic leaves. Annales de l'Institut Fourier, Volume 44 (1994) no. 4, pp. 1237-1242. doi : 10.5802/aif.1432. https://aif.centre-mersenne.org/articles/10.5802/aif.1432/
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