  In this paper we investigate Moishezon twistor spaces which have a structure
of double covering over a very simple rational threefold. These spaces can be
regarded as a direct generalization of the twistor spaces studied by Poon and
Kreussler-Kurke to the case of arbitrary signature. In particular, the branch
divisor of the double covering is a cut of the rational threefold by a single
quartic hypersurface. A defining equation of the hypersurface is determined in
an explicit form. We also show that these twistor spaces interpolate LeBrun
twistor spaces and the twistor spaces constructed in math.DG/0701278.

Differential Geometry;Algebraic Geometry