Algebraic dimension of twistor spaces
type: Item
instance of: scholarly article
title: Algebraic dimension of twistor spaces
zbMATH Open document ID: 0665.32014
DOI: 10.1007/BF01462887
author: Yat-Sun Poon
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164485
review text: 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.
Mathematics Subject Classification ID: 32J99
Mathematics Subject Classification ID: 32L25
zbMATH DE Number: 4088027
zbMATH Keywords: Moishezon space
zbMATH Keywords: twistor space
zbMATH Keywords: self-dual manifold
zbMATH Keywords: self-dual conformal class
reviewed by: Michael K. Murray
MaRDI profile type: Publication
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cites work: Linear field equations on self-dual spaces
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cites work: Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack
OpenAlex ID: W2119238595
description: scientific article; zbMATH DE number 4088027