A complex affine (resp. projective) structure on a complex surface is an atlas of charts with value in (resp. in ) with change of coordinates in the affine group (resp. ). In this paper we classify the affine complex surfaces and calculate, given a complex surface , the space of deformation of affine structures on compatible with its analytic structure. We also show that a projective structure on a complex surface admitting an affine structure is necessarily affine.
Une structure complexe affine (resp. projective) sur une surface complexe est la donnée d’un atlas de cartes à valeur dans (resp. ) à changements de cartes localement constants dans le groupe affine (resp. le groupe ). Dans cet article nous classifions les surfaces complexes affines et calculons, à surface complexe fixée, l’espace de déformation des structures complexes affines sur compatibles avec sa structure analytique. Nous montrons aussi que toute structure projective sur une surface complexe admettant une structure complexe affine est nécessairement affine.
@article{AIF_1998__48_2_441_0, author = {Klingler, Bruno}, title = {Structures affines et projectives sur les surfaces complexes}, journal = {Annales de l'Institut Fourier}, pages = {441--477}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {2}, year = {1998}, doi = {10.5802/aif.1625}, zbl = {0920.32027}, mrnumber = {99c:32038}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1625/} }
TY - JOUR AU - Klingler, Bruno TI - Structures affines et projectives sur les surfaces complexes JO - Annales de l'Institut Fourier PY - 1998 SP - 441 EP - 477 VL - 48 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1625/ DO - 10.5802/aif.1625 LA - fr ID - AIF_1998__48_2_441_0 ER -
%0 Journal Article %A Klingler, Bruno %T Structures affines et projectives sur les surfaces complexes %J Annales de l'Institut Fourier %D 1998 %P 441-477 %V 48 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1625/ %R 10.5802/aif.1625 %G fr %F AIF_1998__48_2_441_0
Klingler, Bruno. Structures affines et projectives sur les surfaces complexes. Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 441-477. doi : 10.5802/aif.1625. https://aif.centre-mersenne.org/articles/10.5802/aif.1625/
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