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

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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 \({\mathbb P}^3\).

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Received October 8, 1996; in final form May 16, 1997

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Campana, F., Kreußler, B. A conic bundle description of Moishezon twistor spaces without effective divisors of degree one. Math Z 229, 137–162 (1998). https://doi.org/10.1007/PL00004646

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  • DOI: https://doi.org/10.1007/PL00004646

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