We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.
Nous étudions la structure analytique des feuilles d’un feuilletage holomorphe par des courbes dans une variété complexe. Nous montrons que si chaque feuille est une surface hyperbolique, alors l’application d’uniformisation est continue. Dans le cas de l’espace projectif complexe il suffit qu’il n’y ait pas de feuille algébrique.
@article{AIF_1995__45_4_1123_0, author = {Candel, Alberto and G\'omez-Mont, X.}, title = {Uniformization of the leaves of a rational vector field}, journal = {Annales de l'Institut Fourier}, pages = {1123--1133}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {4}, year = {1995}, doi = {10.5802/aif.1488}, zbl = {0832.32017}, mrnumber = {96k:32068}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1488/} }
TY - JOUR AU - Candel, Alberto AU - Gómez-Mont, X. TI - Uniformization of the leaves of a rational vector field JO - Annales de l'Institut Fourier PY - 1995 SP - 1123 EP - 1133 VL - 45 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1488/ DO - 10.5802/aif.1488 LA - en ID - AIF_1995__45_4_1123_0 ER -
%0 Journal Article %A Candel, Alberto %A Gómez-Mont, X. %T Uniformization of the leaves of a rational vector field %J Annales de l'Institut Fourier %D 1995 %P 1123-1133 %V 45 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1488/ %R 10.5802/aif.1488 %G en %F AIF_1995__45_4_1123_0
Candel, Alberto; Gómez-Mont, X. Uniformization of the leaves of a rational vector field. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 1123-1133. doi : 10.5802/aif.1488. https://aif.centre-mersenne.org/articles/10.5802/aif.1488/
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