Double solid twistor spaces II: general case

TL;DR

This paper studies a class of Moishezon twistor spaces as double covers over rational threefolds, explicitly characterizing their branch divisors and connecting them to known twistor space families.

Contribution

It generalizes previous twistor space constructions to arbitrary signatures and explicitly determines the defining equations of the branch divisors.

Findings

Explicit form of the branch divisor equation

Connection between these twistor spaces and LeBrun twistor spaces

Interpolation between different twistor space families

Abstract

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 by Poon and Kreussler-Kurke 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. A defining equation of the hypersurface is determined in an explicit form. We also show that these twistor spaces interpolate LeBrun twistor spaces and the twistor spaces constructed in math.DG/0701278.