Moishezon twistor spaces on 4ℂℙ²

Abstract

In this paper we classify all Moishezon twistor spaces on 4 C P 2 4\mathbb {CP}^2 . The classification is given in terms of the structure of the anticanonical system of the twistor spaces. We show that the anticanonical map satisfies one of the following three properties: (a) birational over the image, (b) two-to-one over the image, or (c) the image is 2 2 -dimensional. We determine structure of the images for each case in explicit forms. Then we intensively investigate structure of the twistor spaces in the case (b) and determine the defining equation of the branch divisor of the anticanonical map.