TY - JOUR
T1 - Double solid twistor spaces II
T2 - General case
AU - Honda, Nobuhiro
N1 - Funding Information:
The author was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.
Publisher Copyright:
© De Gruyter 2015.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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 in [J. Differential Geom. 36 (1992), 451-491] and [Compos. Math. 82 (1992), 25-55] 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. We determine a defining equation of the hypersurface in an explicit form. We also show that these twistor spaces interpolate LeBrun twistor spaces and the twistor spaces constructed in [J. Differential Geom. 82 (2009), 411-444].
AB - 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 in [J. Differential Geom. 36 (1992), 451-491] and [Compos. Math. 82 (1992), 25-55] 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. We determine a defining equation of the hypersurface in an explicit form. We also show that these twistor spaces interpolate LeBrun twistor spaces and the twistor spaces constructed in [J. Differential Geom. 82 (2009), 411-444].
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U2 - 10.1515/crelle-2013-0003
DO - 10.1515/crelle-2013-0003
M3 - Article
AN - SCOPUS:84920964633
SP - 181
EP - 220
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 698
ER -