Structures affines et projectives sur les surfaces complexes

Bruno Klingler

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 2, page 441-477
  • ISSN: 0373-0956

Abstract

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A complex affine (resp. projective) structure on a complex surface is an atlas of charts with value in ℂ 2 (resp. in P 2 ℂ ) with change of coordinates in the affine group A ( 2 , ℂ ) (resp. P G L ( 3 , ℂ ) ). In this paper we classify the affine complex surfaces and calculate, given a complex surface S , the space of deformation of affine structures on S compatible with its analytic structure. We also show that a projective structure on a complex surface admitting an affine structure is necessarily affine.

How to cite

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Klingler, Bruno. "Structures affines et projectives sur les surfaces complexes." Annales de l'institut Fourier 48.2 (1998): 441-477. <http://eudml.org/doc/75289>.

@article{Klingler1998,
abstract = {Une structure complexe affine (resp. projective) sur une surface complexe est la donnée d’un atlas de cartes à valeur dans $\{\Bbb C\}^\{2\}$ (resp. $\{\bf P\}^\{2\}\{\Bbb C\}$) à changements de cartes localement constants dans le groupe affine $A(2,\{\Bbb C\})$ (resp. le groupe $\{\bf P\}GL(3,\{\Bbb C\})$). Dans cet article nous classifions les surfaces complexes affines et calculons, à surface complexe $S$ fixée, l’espace de déformation des structures complexes affines sur $S$ compatibles avec sa structure analytique. Nous montrons aussi que toute structure projective sur une surface complexe admettant une structure complexe affine est nécessairement affine.},
author = {Klingler, Bruno},
journal = {Annales de l'institut Fourier},
keywords = {complex surfaces; affine structure; projective structure; flat holomorphic connection; locally homogeneous space},
language = {fre},
number = {2},
pages = {441-477},
publisher = {Association des Annales de l'Institut Fourier},
title = {Structures affines et projectives sur les surfaces complexes},
url = {http://eudml.org/doc/75289},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Klingler, Bruno
TI - Structures affines et projectives sur les surfaces complexes
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 2
SP - 441
EP - 477
AB - Une structure complexe affine (resp. projective) sur une surface complexe est la donnée d’un atlas de cartes à valeur dans ${\Bbb C}^{2}$ (resp. ${\bf P}^{2}{\Bbb C}$) à changements de cartes localement constants dans le groupe affine $A(2,{\Bbb C})$ (resp. le groupe ${\bf P}GL(3,{\Bbb C})$). Dans cet article nous classifions les surfaces complexes affines et calculons, à surface complexe $S$ fixée, l’espace de déformation des structures complexes affines sur $S$ compatibles avec sa structure analytique. Nous montrons aussi que toute structure projective sur une surface complexe admettant une structure complexe affine est nécessairement affine.
LA - fre
KW - complex surfaces; affine structure; projective structure; flat holomorphic connection; locally homogeneous space
UR - http://eudml.org/doc/75289
ER -

References

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