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Algebraic dimension of twistor spaces. (English) Zbl 0665.32014
Associated to any self-dual Riemannian four manifold M is a twistor space. This is the set of all complex structures (compatible with the metric) on all tangent spaces to the manifold. It fibres over the manifold with fibres isomorphic to one dimensional complex projective space and is itself a complex manifold.
The author proves: Theorem. If the twistor space of a compact self-dual manifold is Moishezon, the self-dual conformal class contains a metric with positive scalar curvature.
Reviewer: M.K.Murray

MSC:
32J99 Compact analytic spaces
32L25 Twistor theory, double fibrations (complex-analytic aspects)
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References:
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