Geometry of generic Moishezon twistor spaces on 4CP^2, II: degenerate cases

TL;DR

This paper completes the explicit classification of certain twistor spaces on 4CP^2 by determining the branch divisor's defining equation, building on previous work to fully describe these geometric structures.

Contribution

It provides an explicit form of the branch divisor's defining equation for degenerate Moishezon twistor spaces on 4CP^2, completing the classification.

Findings

Explicit equation of the branch divisor obtained

Complete description of all such twistor spaces achieved

Advances understanding of twistor space geometry on 4CP^2

Abstract

We continue to study twistor spaces on the connected sum of four complex projective planes, whose anticanonical map is of degree two over the image. In particular, we determine the defining equation of the branch divisor of the anticanonical map in an explicit form. Together with previous two articles (arXiv:1009.3153 and arXiv:0705.0060), this completes explicit description of all such twistor spaces.