Uniformization of the leaves of a rational vector field
Annales de l'Institut Fourier, Volume 45 (1995) no. 4, p. 1123-1133

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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {4},
     year = {1995},
     pages = {1123-1133},
     doi = {10.5802/aif.1488},
     zbl = {0832.32017},
     mrnumber = {96k:32068},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_1995__45_4_1123_0/

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