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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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