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Bow varieties and ALF spaces

Published online by Cambridge University Press:  11 December 2014

YUUYA TAKAYAMA
YUUYA TAKAYAMA*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Japan. e-mail: [email protected]
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Abstract

We introduce bow varieties and construct some ALF spaces as bow varieties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 1 , January 2015 , pp. 37 - 82
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

REFERENCES

BiBielawski, R.Hyperkähler structure and group actions. J. Lond. Math. Soc. (2). 55 (1997), 400–414.CrossRefGoogle Scholar
BrBryan, J.Symplectic geometry and the relative Donaldson invariants of $\overline{CP}^2$. Forum. Math.. 9 (1997), 325–365.CrossRefGoogle Scholar
C1Cherkis, S.Instantons on the Taub-NUT space. Adv. Theor. Math. Phys.. 14 (2010), 609–641.CrossRefGoogle Scholar
C2Cherkis, S.Instantons on gravitons. Commun. Math. Phys.. 306 (2011), 449–483.CrossRefGoogle Scholar
DaDancer, A.Dihedral singularities and gravitational instantons. J. Geom. Phys.. 12 (1993), 77–91.CrossRefGoogle Scholar
DSDancer, A. and Swann, A.Hyper-Kähler metrics associated to compact Lie groups. Math. Proc. Camb. Phil. Soc.. 120 (1996), 61–69.CrossRefGoogle Scholar
DoDonaldson, S.Nahm's equations and the classification of monopoles. Commun. Math. Phys.. 96 (1984), 387–407.CrossRefGoogle Scholar
GNGocho, T. and Nakajima, H.Einstein-Hermitian connections on hyper-Kähler quotients. J. Math. Soc. 44–1 (1992), 43–51.Google Scholar
HKLRHitchin, N., Karlhede, A., Lindström, U. and Rocek, M.Hyper-kähler metrics and supersymmetry. Commun. Math. Phys.. 108 (1987), 535–589.CrossRefGoogle Scholar
KinKing, A.Moduli of representations of finite dimensional algebras. Quarterly J. of Math.. 45 (1994), 515–530.CrossRefGoogle Scholar
KiKirwan, F.Cohomology of Quotients in Symplectic and Algebraic Geometryt (Princeton University Press, 1984).Google Scholar
Kr1Kronheimer, P. A hyper-kähler structure on the cotangent bundle of a complex Lie group. arXiv:math/0409253v1.Google Scholar
Kr2Kronheimer, P.The construction of ALE spaces as hyper-Kähler quotients. J. Diff. Geom.. 29 (1989), 665–683.Google Scholar
KNKronheimer, P. and Nakajima, H.Yang-Mills instantons on ALE Gravitational instantons. Math. Ann. 288–2 (1990), 263–307.CrossRefGoogle Scholar
MMinerbe, V. On some asymptotically flat manifolds with non maximal volume growth. arXiv:0709.1084v1.Google Scholar
MFKMumford, D., Fogarty, J. and Kirwan, F.Geometric Invariant Theory (Springer Verlag, 1994).CrossRefGoogle Scholar
Na1Nakajima, H.Instantons on ALE spaces, quiver varieties, and Kac–Moody algebras. Duke Math. J. 76–2 (1994), 365–416.CrossRefGoogle Scholar
Na2Nakajima, H.Lectures on Hilbert Schemes of Points on Surfaces (American Mathematical Society, 1999).CrossRefGoogle Scholar
NeNeeman, A.The topology of quotient varieties. Ann. of Math. 103–2 (1985), 419–459.CrossRefGoogle Scholar
VVaradarajan, V.Lie groups, Lie algebras, and their representations (Prentice-Hall, inc).CrossRefGoogle Scholar