no. 2
Structures affines et projectives sur les surfaces complexes
Annales de l'Institut Fourier, Tome 48 (1998) no. 2, pp. 441-477.

Une structure complexe affine (resp. projective) sur une surface complexe est la donnée d’un atlas de cartes à valeur dans ℂ 2 (resp. P 2 ℂ) à changements de cartes localement constants dans le groupe affine A(2,ℂ) (resp. le groupe PGL(3,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.

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. PGL(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.

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     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},
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Klingler, Bruno. Structures affines et projectives sur les surfaces complexes. Annales de l'Institut Fourier, Tome 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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