Moishezon twistor spaces on 4CP^2

TL;DR

This paper classifies all Moishezon twistor spaces on 4CP^2 based on their anticanonical systems, detailing their structures and explicit forms, especially focusing on the case where the anticanonical map is two-to-one.

Contribution

It provides a complete classification of Moishezon twistor spaces on 4CP^2 using anticanonical system analysis, including explicit descriptions and equations.

Findings

Anticanonical map is either birational, two-to-one, or has a two-dimensional image.

Explicit forms of the images for each case are determined.

The branch divisor equation is explicitly derived for the two-to-one case.

Abstract

In this paper we classify all Moishezon twistor spaces on 4CP^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 two-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.