no. 7
Un théorème de Green presque complexe
Annales de l'Institut Fourier, Tome 54 (2004) no. 7, pp. 2357-2367.

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.

DOI : https://doi.org/10.5802/aif.2082
Classification : 32H25,  32Q45,  32Q60
Mots clés : hyperbolicité, théorèmes de type Picard, courbes pseudoholomorphes 
@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},
     pages = {2357--2367},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {7},
     year = {2004},
     doi = {10.5802/aif.2082},
     zbl = {1076.32020},
     mrnumber = {2139696},
     language = {fr},
     url = {http://www.numdam.org/articles/10.5802/aif.2082/}
}
TY  - JOUR
AU  - Duval, Julien
TI  - Un théorème de Green presque complexe
JO  - Annales de l'Institut Fourier
PY  - 2004
DA  - 2004///
SP  - 2357
EP  - 2367
VL  - 54
IS  - 7
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2082/
UR  - https://zbmath.org/?q=an%3A1076.32020
UR  - https://www.ams.org/mathscinet-getitem?mr=2139696
UR  - https://doi.org/10.5802/aif.2082
DO  - 10.5802/aif.2082
LA  - fr
ID  - AIF_2004__54_7_2357_0
ER  - 
Duval, Julien. Un théorème de Green presque complexe. Annales de l'Institut Fourier, Tome 54 (2004) no. 7, pp. 2357-2367. doi : 10.5802/aif.2082. http://www.numdam.org/articles/10.5802/aif.2082/

[1] M. Audin; J. Lafontaine ed. Holomorphic curves in symplectic geometry, Progress in Math, 117, Birkhäuser, Basel, 1994 | MR 1274923 | Zbl 0802.53001

[2] F. Berteloot; J. Duval Sur l'hyperbolicité de certains complémentaires, Ens. Math, Volume 47 (2001), pp. 253-267 | MR 1876928 | Zbl 1009.32015

[3] R. Brody Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., Volume 235 (1978), pp. 213-219 | MR 470252 | Zbl 0416.32013

[4] R. Debalme; S. Ivashkovich Complete hyperbolic neighborhoods in almost-complex surfaces, Int. J. of Math, Volume 12 (2001), pp. 211-221 | Article | MR 1823575 | Zbl 01629375

[5] M. Green Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math., Volume 97 (1975), pp. 43-75 | Article | MR 367302 | Zbl 0301.32022

[6] M. Gromov Pseudo holomorphic curves in symplectic manifolds, Invent. Math., Volume 82 (1985), pp. 307-347 | Article | Zbl 0592.53025

[7] S. Kobayashi Hyperbolic complex spaces, Grund. der math. Wiss, 318, Springer, Berlin, 1998 | MR 1635983 | Zbl 0917.32019

[8] B. Kruglikov; M. Overholt Pseudoholomorphic mappings and Kobayashi hyperbolicity, Diff. Geom. Appl., Volume 11 (1999), pp. 265-277 | Article | MR 1726542 | Zbl 0954.32019

[9] O. Lehto; K.I. Virtanen Quasiconformal mappings in the plane, Grund. der math. Wiss, 126, Springer, Berlin, 1973 | MR 344463 | Zbl 0267.30016

[10] J.-C. Sikorav Dual elliptic planes (2000) (preprint, arXiv math.SG/0008234) | MR 2145943 | Zbl 1072.32018

Cité par Sources :