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Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes

Author(s): F. Campana; B. Kreußler
Journal: Proc. Amer. Math. Soc. 127 (1999), 2633-2642.
MSC (1991): Primary 32L25, 32J17, 32J20
Posted: May 19, 1999
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Abstract: We prove the existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes $4 \mathbb{C}\mathbb{P}^2$. These are the first examples of twistor spaces of algebraic dimension two over a simply connected Riemannian four-manifold with positive scalar curvature. For this purpose we develop a method to distinguish between twistor spaces of algebraic dimension one and two by looking at the order of a certain point in the Picard group of an elliptic curve.

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Additional Information:

F. Campana
Affiliation: Department of Mathematics, Université de Nancy, F--54506 Vandouvre les Nancy, France
Email: Frederic.Campana@iecn.u-nancy.fr

B. Kreußler
Affiliation: Department of Mathematics, Universität Kaiserslautern, D--67653 Kaiserslautern, Germany
Email: kreusler@mathematik.uni-kl.de

DOI: 10.1090/S0002-9939-99-05406-4
PII: S 0002-9939(99)05406-4
Received by editor(s): June 20, 1996
Posted: May 19, 1999
Communicated by: Ron Donagi
Copyright of article: Copyright 1999, American Mathematical Society

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