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

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.


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
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