On a construction of the twistor spaces of Joyce metrics, II
Nobuhiro HONDA
Source: J. Math. Soc. Japan Volume 61, Number 4
(2009), 1243-1260.
Abstract
In this note, we explicitly construct the twistor spaces of some Joyce metrics on the connected sum of arbitrary number of complex projective planes. Unlike our former construction for the case of four complex projective planes, the present construction mainly utilizes minitwistor spaces, and partially follows the method and construction given in [5] and [6].
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Keywords: twistor space; minitwistor space; Moishezon manifold; conic bundle; bimeromorphic transformation; self-dual metric
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1257520506
Digital Object Identifier: doi:10.2969/jmsj/06141243
Mathematical Reviews number (MathSciNet): MR2424925
Zentralblatt MATH identifier: 05651150
References
M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London, Ser. A, 362 (1978), 425–461.
Mathematical Reviews (MathSciNet): MR506229
Digital Object Identifier: doi:10.1098/rspa.1978.0143
A. Fujiki, Compact self-dual manifolds with torus actions, J. Differential Geom., 55 (2000), 229–324.
Mathematical Reviews (MathSciNet): MR1847312
Zentralblatt MATH: 1032.57036
Project Euclid: euclid.jdg/1090340879
N. Hitchin, Complex manifolds and Einstein's equations, Lecture Notes in Math., Springer, 970 (1982), pp. 73–99.
Mathematical Reviews (MathSciNet): MR699802
Zentralblatt MATH: 0507.53025
Digital Object Identifier: doi:10.1007/BFb0066025
N. Honda, On a construction of the twistor spaces of Joyce metrics, J. Algebraic Geom., 17 (2008), 709–750, available as math.DG/0603242 and math.DG/0604306.
N. Honda, Explicit construction of new Moishezon twistor spaces, J. Differential Geom., 82 (2009), 411–444.
Mathematical Reviews (MathSciNet): MR2520798
Zentralblatt MATH: 1183.53043
Project Euclid: euclid.jdg/1246888490
N. Honda, A new series of compact minitwistor spaces and Moishezon twistor spaces over them, to appear in J. Reine Angew. Math.
Mathematical Reviews (MathSciNet): MR2658186
N. Honda, Projective models of the twistor spaces of Joyce metrics, preprint, arXiv:0805:0046.
D. Joyce, Explicit construction of self-dual 4-manifolds, Duke Math. J., 77 (1995), 519–552.
Mathematical Reviews (MathSciNet): MR1324633
Zentralblatt MATH: 0855.57028
Digital Object Identifier: doi:10.1215/S0012-7094-95-07716-3
Project Euclid: euclid.dmj/1077286532
C. LeBrun, Explicit self-dual metrics on $\mbi{CP}^{2} \# \cdots \# \mbi{CP}^{2}$, J. Differential Geom., 34 (1991), 223–253.
Mathematical Reviews (MathSciNet): MR1114461
Zentralblatt MATH: 0725.53067
Project Euclid: euclid.jdg/1214446999
Journal of the Mathematical Society of Japan
