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Double solid twistor spaces. II: General case. (English) Zbl 1316.32015
The author studies Moishezon twistor spaces which have the structure of a double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied in [Y. S. Poon, J. Differ. Geom. 36, No. 2, 451–491 (1992; Zbl 0742.53024)] and [B. Kreußler et al., Compos. Math. 82, No. 1, 25–55 (1992; Zbl 0766.53049)] 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. The author determines a defining equation of the hypersurface in an explicit form. He also shows that these twistor spaces interpolate the LeBrun twistor spaces and the twistor spaces constructed in [N. Honda, J. Differ. Geom. 82, No. 2, 411–444 (2009; Zbl 1183.53043)].

MSC:
32L25 Twistor theory, double fibrations (complex-analytic aspects)
32G05 Deformations of complex structures
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
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