Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes
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- by F. Campana and B. Kreußler PDF
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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.References
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Additional Information
- F. Campana
- Affiliation: Department of Mathematics, Université de Nancy, F–54 506 Vandœuvre les Nancy, France
- Email: Frederic.Campana@iecn.u-nancy.fr
- B. Kreußler
- Affiliation: Department of Mathematics, Universität Kaiserslautern, D–67 653 Kaiserslautern, Germany
- Email: kreusler@mathematik.uni-kl.de
- Received by editor(s): June 20, 1996
- Published electronically: May 19, 1999
- Communicated by: Ron Donagi
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2633-2642
- MSC (1991): Primary 32L25, 32J17, 32J20
- DOI: https://doi.org/10.1090/S0002-9939-99-05406-4
- MathSciNet review: 1676299