## On twistor spaces of the class $${\mathcal C}$$.(English)Zbl 0694.32017

A (very) special case of the main result of this paper is the simple connectedness of any Moishezon manifold Z containing a smooth rational curve C with ample normal bundle $$N_{C| Z}$$. When Z is unirational, this is due to J. P. Serre.
As an application, only $$S^ 4$$ and connected sums of $${\mathbb{C}}{\mathbb{P}}_ 2's$$ can have Moishezon twistor spaces. Recent examples of C. Lebruin and then H. Kurke show that this is sharp.
Reviewer: F.Campana

### MSC:

 32L25 Twistor theory, double fibrations (complex-analytic aspects) 32J10 Algebraic dependence theorems
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