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The class \({\mathcal C}\) is not stable by small deformations. (English) Zbl 0722.32014
We show that some Lebrun-Moishezon twistor spaces have arbitrarily small deformations which are not in Fujiki’s class \({\mathcal C}\) (i.e. bimeromorphic to compact Kähler manifolds).
Reviewer: F.Campana

32J27 Compact Kähler manifolds: generalizations, classification
32J99 Compact analytic spaces
32L25 Twistor theory, double fibrations (complex-analytic aspects)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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