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

摘要

In [K2] Moishezon twister spaces over the connected sum nCP(2) (n greater than or equal to 4), which do not contain effective divisors of degree one, were constructed as deformations of the twister spaces introduced in [LeB]. We study their structure for n greater than or equal to 4 by constructing a modification which is a conic bundle over 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 P-3. [References: 17]