Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On a construction of the twistor spaces of Joyce metrics


Author: Nobuhiro Honda
Journal: J. Algebraic Geom. 17 (2008), 709-750
DOI: https://doi.org/10.1090/S1056-3911-08-00474-8
Published electronically: February 20, 2008
MathSciNet review: 2424925
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Abstract | References | Additional Information

Abstract: We explicitly construct the twistor spaces of some self-dual metrics with torus action given by D. Joyce. Starting from a fiber space over a projective line whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the desired twistor spaces. These constructions are based on a detailed analysis of the anticanonical system of the twistor spaces.


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Additional Information

Nobuhiro Honda
Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro, 152-8551, Japan
Email: honda@math.titech.ac.jp

DOI: https://doi.org/10.1090/S1056-3911-08-00474-8
Received by editor(s): July 9, 2006
Received by editor(s) in revised form: November 30, 2006
Published electronically: February 20, 2008

American Mathematical Society