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ISSN 1088-6850(e) ISSN 0002-9947(p)

Non-Moishezon twistor spaces of $4{\mathbf{CP}}^2$ with non-trivial automorphism group

Author: Nobuhiro Honda
Journal: Trans. Amer. Math. Soc. 358 (2006), 1897-1920
MSC (2000): Primary 32L25, 32G05, 32G07, 53A30, 53C25
Posted: December 20, 2005
MathSciNet review: 2197434
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a twistor space of a self-dual metric on $4{\mathbf{CP}}^2$ with -isometry is not Moishezon iff there is a $\mathbf{C}^*$ -orbit biholomorphic to a smooth elliptic curve, where the $\mathbf C^*$ -action is the complexification of the -action on the twistor space. It follows that the -isometry has a two-sphere whose isotropy group is $\mathbf Z_2$ . We also prove the existence of such twistor spaces in a strong form to show that a problem of Campana and Kreußler is affirmative even though a twistor space is required to have a non-trivial automorphism group.

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