Projectively flat surfaces and Bogomolov's theorem on class VII_0 - surfaces

Andrei Teleman (1)

1 Institut für Mathematik [Zürich]

We give a complete proof of Bogomolov's theorem on class VII0 surfaces starting with the idea of Li, Yau and Zheng to use Kobayashi-Hitchin correspondence. We show that, because of the non-topological character of Gauduchon's degree, the proof of these authors is not complete. We prove that any projectively flat hermitian surface is locally conformally flat-Kähler, which reduces the problem to the classification of locally conformally flat-Kähler surfaces.

Mots clés: complex surface; class VII; Hermite-Einstein; Kobayashi-Hitchin; Hitchin-Kobayashi

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Andrei Teleman. Projectively flat surfaces and Bogomolov's theorem on class VII_0 - surfaces. International Journal of Mathematics, 1994, 5 (2), pp.253-264. ⟨10.1142/S0129167X94000152⟩. ⟨hal-00881780⟩