Double solid twistor spaces: The case of arbitrary signature

Nobuhiro Honda

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7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)463-504
Number of pages42
JournalInventiones Mathematicae
Issue number3
Publication statusPublished - 2008 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)


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