On montre l'hyperbolicité du complémentaire de cinq droites en position générale dans un plan projectif presque complexe, répondant ainsi à une question de S. Ivashkovich.
We prove the hyperbolicity of the complement of five lines in general position in an almost complex projective plane, answering a question by S. Ivashkovich.
@article{AIF_2004__54_7_2357_0, author = {Duval, Julien}, title = {Un th\'eor\`eme de Green presque complexe}, journal = {Annales de l'Institut Fourier}, volume = {54}, year = {2004}, pages = {2357-2367}, doi = {10.5802/aif.2082}, mrnumber = {2139696}, zbl = {1076.32020}, language = {fr}, url = {http://dml.mathdoc.fr/item/AIF_2004__54_7_2357_0} }
Duval, Julien. Un théorème de Green presque complexe. Annales de l'Institut Fourier, Tome 54 (2004) pp. 2357-2367. doi : 10.5802/aif.2082. http://gdmltest.u-ga.fr/item/AIF_2004__54_7_2357_0/
[1] Holomorphic curves in symplectic geometry, Birkhäuser, Basel, Progress in Math, Tome 117 (1994) | MR 1274923 | Zbl 0802.53001
[2] Sur l'hyperbolicité de certains complémentaires, Ens. Math, Tome 47 (2001), pp. 253-267 | MR 1876928 | Zbl 1009.32015
[3] Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., Tome 235 (1978), pp. 213-219 | MR 470252 | Zbl 0416.32013
[4] Complete hyperbolic neighborhoods in almost-complex surfaces, Int. J. of Math, Tome 12 (2001), pp. 211-221 | Article | MR 1823575 | Zbl 01629375
[5] Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math., Tome 97 (1975), pp. 43-75 | Article | MR 367302 | Zbl 0301.32022
[6] Pseudo holomorphic curves in symplectic manifolds, Invent. Math., Tome 82 (1985), pp. 307-347 | Article | Zbl 0592.53025
[7] Hyperbolic complex spaces, Springer, Berlin, Grund. der math. Wiss, Tome 318 (1998) | MR 1635983 | Zbl 0917.32019
[8] Pseudoholomorphic mappings and Kobayashi hyperbolicity, Diff. Geom. Appl., Tome 11 (1999), pp. 265-277 | Article | MR 1726542 | Zbl 0954.32019
[9] Quasiconformal mappings in the plane, Springer, Berlin, Grund. der math. Wiss, Tome 126 (1973) | MR 344463 | Zbl 0267.30016
[10] Dual elliptic planes (2000) (preprint, arXiv math.SG/0008234) | MR 2145943 | Zbl 1072.32018