Twistor spaces over the connected sum of 3 projective planes. (English) Zbl 0766.53049

Kreußler, Bernd; Kurke, Herbert

Compos. Math. 82, No. 1, 25-55 (1992).

The paper gives an algebraic-geometric description of complex twistor spaces of the connected sum of three complex projective planes. This is done by considering the map defined by the half anticanonical linear system on the complex twistor space of a 4-dimensional manifold satisfying the following assumption: The underlying self-dual structure on the 4-dimensional manifold has a metric of positive scalar curvature in its conformal class. If the half anticanonical linear system has no base points then the twistor space is a modification of a certain conic bundle over a quadric surface. In the other case there is a family of twistor spaces which are double solids.

Reviewer: H.-B.Rademacher (Bonn)

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
32L25	Twistor theory, double fibrations (complex-analytic aspects)

Keywords:

half anticanonical linear system; complex twistor spaces; complex projective planes; self-dual structure

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