Mathematische Zeitschrift

, Volume 229, Issue 1, pp 137–162

A conic bundle description of Moishezon twistor spaces without effective divisors of degree one

  • F. Campana
  • B. Kreußler

DOI: 10.1007/PL00004646

Cite this article as:
Campana, F. & Kreußler, B. Math Z (1998) 229: 137. doi:10.1007/PL00004646

Abstract.

In [K2] Moishezon twistor spaces over the connected sum \(n{\mathbb{CP}}^2\) (\(n\geq 4\)), which do not contain effective divisors of degree one, were constructed as deformations of the twistor spaces introduced in [LeB]. We study their structure for \(n\geq 4\) by constructing a modification which is a conic bundle over \({\mathbb P}^2\). We show that they are rational. In case n = 4 we give explicit equations for such conic bundles and use them to construct explicit birational maps between these conic bundles and \({\mathbb P}^3\).

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • F. Campana
    • 1
  • B. Kreußler
    • 2
  1. 1. Université de Nancy, F-54506 Vandœuvre les Nancy, France (e-mail: Frederic.Campana@iecn.u-nancy.fr) FR
  2. 2. FB Mathematik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany (e-mail: kreusler@mathematik.uni-kl.de) DE

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