Surfaces of the class VII\(_0\) admitting a vector field. (Surfaces de la classe VII\(_0\) admettant un champ de vecteurs.) (French) Zbl 0984.32009

Dloussky, Georges; Oeljeklaus, Karl; Toma, Matei

Comment. Math. Helv. 75, No. 2, 255-270 (2000).

The authors prove that a compact complex surface of class \(\text{VII}_0\) with \(b_2>0\) admitting an action of \((\mathbb{C},+)\) contains exactly \(b_2\) rational curves. It follows that the surface is a deformation of a blown-up primary Hopf surface.

Reviewer: P.E.Newstead (Liverpool)

MSC:

32J15	Compact complex surfaces
32M05	Complex Lie groups, group actions on complex spaces
32S65	Singularities of holomorphic vector fields and foliations
57R30	Foliations in differential topology; geometric theory

Keywords:

holomorphic foliation; holomorphic vector fields; compact complex surface