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Une caractérisation des surfaces d’Inoue-Hirzebruch. (A characterization of Inoue-Hirzebruch surfaces). (French) Zbl 0993.32013
A surface considered in this paper is a smooth complex manifold of dimension 2. An Inoue-Hirzebruch surface $$S$$ is a surface of class $$VII_{0}$$ (i.e. that does not contain a smooth rational curve of self-intersection $$-1$$ and has the first Betti number $$b_{1}(S)=1$$) with the second Betti number $$b_{2}(S)>0$$, whose maximal divisor $$D_{\max}$$ consists of $$b_{2}$$ linearly independent rational curves in $$H_{2}(S,Q)$$ formed by one or two cycles.
This paper gives a characterization of the Inoue-Hirzebruch surfaces in terms of the following theorem: Let $$S$$ be a surface of the class $$VII_{0}$$ with $$b_{2}(S)>0$$, then $$S$$ is an Inoue-Hirzebruch surface, if and only if $$S$$ admits two twisted vector fields, not collinear in at least one point.

##### MSC:
 32J15 Compact complex surfaces 32S25 Complex surface and hypersurface singularities 37F75 Dynamical aspects of holomorphic foliations and vector fields
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