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.
References
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References
- A. Fujiki, Compact self-dual manifolds with torus actions, J. Diff. Geom. 55 (2000), 229β324. MR 1847312 (2002k:57085)
- N. Hitchin, Linear field equations on self-dual spaces, Proc. London Math. Soc. 370 (1980), 173β191. MR 563832 (81i:81057)
- D. Joyce, Explicit construction of self-dual $4$-manifolds, Duke Math. J. 77 (1995), 519β552. MR 1324633 (96d:53049)
- C. LeBrun, Explicit self-dual metrics on ${\mathbf {CP}}^2\#\cdots \#{\mathbf {CP}}^2$, J. Diff. Geom. 34 (1991), 223β253. MR 1114461 (92g:53040)
- C. LeBrun, Self-dual manifolds and hyperbolic geometry, Einstein metrics and Yang-Mills connections (Sanda, 1990), Lecture Notes in Pure and Appl. Math. 145 (1993), 99β131. MR 1215284 (94h:53060)
- T. Oda, βConvex Bodies and Algebraic Geometryβ, Ergebnisse der Math., Springer-Verlag, Berlin, 1988. MR 922894 (88m:14038)
- P. Orlik, F. Raymond, Actions of the torus on $4$-manifolds, I, Trans. Amer. Math. Soc. 152 (1970), 531β559. MR 0268911 (42:3808)
- H. Pedersen, Y. S. Poon, Equivariant connected sums of compact self-dual manifolds, Math. Ann. 301 (1995), 717β749. MR 1326765 (95m:53069)
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
Received by editor(s):
July 9, 2006
Received by editor(s) in revised form:
November 30, 2006
Published electronically:
February 20, 2008
