# Double solid twistor spaces: The case of arbitrary signature

Nobuhiro Honda

7 被引用数 (Scopus)

## 抄録

In a recent paper ([9]) we constructed a series of new Moishezon twistor spaces which are a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on n CP 2 for arbitrary n ≥ 3, which can be regarded as a generalization of the twistor spaces of 'double solid type' on 3CP 2 studied by Kreußler, Kurke, Poon and the author. Similarly to the twistor spaces of 'double solid type' on 3CP 2, projective models of the present twistor spaces have a natural structure of double covering of a CP 2-bundle over CP 1. We explicitly give a defining polynomial of the branch divisor of the double covering, whose restriction to fibers is degree four. If n ≥ 4 these are new twistor spaces, to the best of the author's knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from [9], the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.

本文言語 English 463-504 42 Inventiones Mathematicae 174 3 https://doi.org/10.1007/s00222-008-0139-5 Published - 2008 12 1

• 数学 (全般)

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