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

#### Citation

Campana, F. and Kreussler B. (1999) ‘Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes’, Proceedings of the AMS 127(9) 2633-2642.

##### Date

1999##### Author

Campana, Frederic

Kreussler, Bernd

##### Peer Reviewed

Yes##### Metadata

Show full item record*Campana, F. and Kreussler B. (1999) ‘Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes’, Proceedings of the AMS 127(9) 2633-2642.*

##### Abstract

We prove the existence of twistor spaces of algebraic dimension
two over the connected sum of four complex projective planes 4CP2. These are
the rst 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.

##### Keywords

MathematicsTwistor spaces

Algebraic dimension