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Surfaces of the class VII$$_0$$ admitting a vector field. II. (Surfaces de la classe $$\text{VII}_0$$ admettant un champ de vecteurs. II.) (French) Zbl 1011.32014
Translation of the French summary: We finish the classification of compact holomorphic surfaces for which a nontrivial global holomorphic vector field exists. We prove, under this hypothesis, that every surface $${\mathcal S}$$ of the class $$\text{VII}_0$$ with $$b_2({\mathcal S})>0$$ contains a global spherical shell. That is exactly the case where this classification was incomplete.
 32J15 Compact complex surfaces 32Q57 Classification theorems for complex manifolds 32M25 Complex vector fields, holomorphic foliations, $$\mathbb{C}$$-actions