Moishezon twistor spaces on 4ℂℙ²

Honda, Nobuhiro

doi:10.1090/S1056-3911-2013-00619-0

Moishezon twistor spaces on $4\mathbb {CP}^2$

Author: Nobuhiro Honda
Journal: J. Algebraic Geom. 23 (2014), 471-538
DOI: https://doi.org/10.1090/S1056-3911-2013-00619-0
Published electronically: October 15, 2013
Previous version: Original version posted October 10, 2013
Corrected version: Current version corrects compositor's error regarding the received dates of this paper
MathSciNet review: 3205589
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Abstract | References | Additional Information

Abstract: In this paper we classify all Moishezon twistor spaces on $4\mathbb {CP}^2$. 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 $2$-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.

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Additional Information

Nobuhiro Honda
Affiliation: Mathematical Institute, Tohoku University, Sendai, Miyagi, Japan
Email: honda@math.tohoku.ac.jp

Received by editor(s): April 18, 2011
Received by editor(s) in revised form: December 19, 2011, and April 24, 2012
Published electronically: October 15, 2013
Additional Notes: The author was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.