Open AccessMoishezon twistor spaces on 4ℂℙ²
Author(s) -
Nobuhiro Honda
Publication year - 2013
Publication title -
journal of algebraic geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.824
H-Index - 50
eISSN - 1534-7486
pISSN - 1056-3911
DOI - 10.1090/s1056-3911-2013-00619-0
Subject(s) - algorithm , annotation , twistor theory , mathematics , type (biology) , artificial intelligence , computer science , database , pure mathematics , geology , paleontology
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.