Geomety of generic Moishezon twistor spaces on 4CP^2

Details Geomety of generic Moishezon twistor spaces on 4CP^2 Geomety of generic Moishezon twistor spaces on 4CP^2

2010-09-16

arxiv.org/abs/1009.3153v1

Mathematics

Differential Geometry

31 pages, 5 figures

Scientific paper

In this paper we investigate a family of Moishezon twistor spaces on the connected sum of 4 complex projective planes, which can be regarded as a direct generalization of the twistor spaces on 3CP^2 of double solid type studied by Poon and Kreussler-Kurke. These twistor spaces have a natural structure of double covering over a scroll of 2-planes over a conic. We determine the defining equations of the branch divisors in an explicit form, which are very similar to the case of 3CP^2. Using these explicit description we compute the dimension of the moduli spaces of these twistor spaces. Also we observe that similarly to the case of 3CP^2, these twistor spaces can also be considered as generic Moishezon twistor spaces on 4CP^2. We obtain these results by analyzing the anticanonical map of the twistor spaces in detail, which enables us to give an explicit construction of the twistor spaces, up to small resolutions.

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