Classification of Moishezon twistor spaces on 4CP^2

TL;DR

This paper classifies all Moishezon twistor spaces on 4CP^2 using the anticanonical system, detailing the structure of their anticanonical maps and images.

Contribution

It provides a complete classification of Moishezon twistor spaces on 4CP^2 based on the properties of their anticanonical maps.

Findings

Anticanonical map is either birational, two-to-one, or maps onto a rational surface.

Explicit descriptions of the images of the anticanonical map in each case.

Structural insights into Moishezon twistor spaces on 4CP^2.

Abstract

In this paper we provide a classification of all Moishezon twistor spaces on the connected sum of four complex projective planes. This is given by means of the anticanonical system of the twistor spaces. In particular, we show that the anticanonical map is birational, two to one over the image, or otherwise the image of the anticanonical map is a rational surface. We also obtain the structure of the images of the anticanonical map in each of the three cases in explicit forms.