Algebraic dimension of twistor spaces
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.
scientific article; zbMATH DE number 4088027