Double Solid Twistor Spaces: the Case of Arbitrary Signature

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 nCP for arbitrary n ≥ 3, which can be regarded as a generalization of the twistor spaces of ‘double solid type’ on 3CP studied by Kreußler, Kurke, Poon and the author. Similarly to the twistor spaces of ‘double solid type’ on 3CP, projective models of the present twistor spaces have a natural structure of double covering of a CP-bundle over CP. 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.