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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.
This article is the continuation of Part I [ibid. 75, No. 2, 255-270 (2000; Zbl 0984.32009)].

MSC:
32J15 Compact complex surfaces
32Q57 Classification theorems for complex manifolds
32M25 Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions
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