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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.

##### 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
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