An almost complex version of a theorem by Green

Julien Duval[1]

  • [1] Université Paul Sabatier, laboratoire Émile Picard, UMR CNRS 5580, 31062 Toulouse Cedex 4 (France)

Annales de l'Institut Fourier (2004)

  • Volume: 54, Issue: 7, page 2357-2367
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Duval, Julien. "Un théorème de Green presque complexe." Annales de l'Institut Fourier 54.7 (2004): 2357-2367. <http://eudml.org/doc/116175>.

@article{Duval2004,
abstract = {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.},
affiliation = {Université Paul Sabatier, laboratoire Émile Picard, UMR CNRS 5580, 31062 Toulouse Cedex 4 (France)},
author = {Duval, Julien},
journal = {Annales de l'Institut Fourier},
keywords = {Hyperbolicity; Picard-type theorems; pseudoholomorphic curves},
language = {fre},
number = {7},
pages = {2357-2367},
publisher = {Association des Annales de l'Institut Fourier},
title = {Un théorème de Green presque complexe},
url = {http://eudml.org/doc/116175},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Duval, Julien
TI - Un théorème de Green presque complexe
JO - Annales de l'Institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 7
SP - 2357
EP - 2367
AB - 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.
LA - fre
KW - Hyperbolicity; Picard-type theorems; pseudoholomorphic curves
UR - http://eudml.org/doc/116175
ER -

References

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  1. M. Audin, J. Lafontaine ed., Holomorphic curves in symplectic geometry, 117 (1994), Birkhäuser, Basel Zbl0802.53001MR1274923
  2. F. Berteloot, J. Duval, Sur l'hyperbolicité de certains complémentaires, Ens. Math 47 (2001), 253-267 Zbl1009.32015MR1876928
  3. R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc. 235 (1978), 213-219 Zbl0416.32013MR470252
  4. R. Debalme, S. Ivashkovich, Complete hyperbolic neighborhoods in almost-complex surfaces, Int. J. of Math 12 (2001), 211-221 Zbl1110.32306MR1823575
  5. M. Green, Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math. 97 (1975), 43-75 Zbl0301.32022MR367302
  6. M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347 Zbl0592.53025
  7. S. Kobayashi, Hyperbolic complex spaces, 318 (1998), Springer, Berlin Zbl0917.32019MR1635983
  8. B. Kruglikov, M. Overholt, Pseudoholomorphic mappings and Kobayashi hyperbolicity, Diff. Geom. Appl. 11 (1999), 265-277 Zbl0954.32019MR1726542
  9. O. Lehto, K.I. Virtanen, Quasiconformal mappings in the plane, 126 (1973), Springer, Berlin Zbl0267.30016MR344463
  10. J.-C. Sikorav, Dual elliptic planes, (2000) Zbl1072.32018MR2145943

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