Structures affines et projectives sur les surfaces complexes. (Affine and projective structures on complex surfaces). (French) Zbl 0920.32027

Klingler, Bruno

Ann. Inst. Fourier 48, No. 2, 441-477 (1998).

It is known by works of M. Inoue, S. Kobayashi and T. Ochiai [J. Fac. Sci. Univ. Tokyo, Sect. I A 27, 247-264 (1980; Zbl 0467.32014)] that admitting a holomorphic connection is biholomorphically to either a complex torus or a Kodaira’s surface or a Hopf’s affine surface or an Inoue’s surface or a holomorphic principal fiber over a closed Riemann surface of genus greater or equal to two, with odd first Betti number. They prove that such a surface has a complex affine structure. The author proceeds to describe in a geometric way all complex affine surfaces and for each fixed one all such structures which are compatible with its analytic structure.

Reviewer: R.A.Hidalgo (Valparaiso)

MSC:

32J15	Compact complex surfaces
57M50	General geometric structures on low-dimensional manifolds

Keywords:

complex surfaces; affine structure; projective structure; flat holomorphic connection; locally homogeneous space

Citations:

Zbl 0467.32014

References:

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