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

Campana, F.

J. Differ. Geom. 33, No. 2, 541-549 (1991).

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

Keywords:

fundamental group; simple connectedness of any Moishezon manifold; twistor spaces