Einstein-Hermitian connections on Hyper-Kähler quotients

Toru GOCHO; Hiraku NAKAJIMA

doi:10.2969/jmsj/04410043

Toru GOCHO, Hiraku NAKAJIMA

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 1 Pages 43-51

DOI https://doi.org/10.2969/jmsj/04410043

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Published: 1992 Received: May 11, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Tadashi Nagano on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Toru GOCHO¹⁾, Hiraku NAKAZIMA¹⁾
Right : Toru GOCHO¹⁾, Hiraku NAKAJIMA¹⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987.
2) P. J. Braam and P, van Baal, Nahm's transformation for instantons, Comm. Math. Phys., 122 (1989), 267-280.
3) D. S. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, MSRI Publ., 1, Springer-Verlag, 1984.
4) K. Galicki and H. B. Lawson, Quaternionic reduction and quaternionic orbifolds,Math. Ann., 282 (1988), 1-21.
5) N. J. Hitchin, Metrics on moduli spaces, in Proceedings of the Lefschez Centennial Conference (Contemporary Math, 58, Part I), A. M. S., Providence, R. I., 1986.
6) N. J. Hitchin, A. Karlhede, U. Lindström and M. Rocek, Hyperkähler metrics and supersymmetry, Comm. Math. Phys., 108 (1987), 535-589.
7) M. Itoh, Gauge fields and quaternion structure, Kodai Math. J., 11 (1988), 344-360.
8) P. B. Kronheimer, The construction of ALE spaces as hyper-kähler quotients, J. Diff. Geom., 29 (1989), 665-683.
9) P. B. Kronheimer and H. Nakajima, Yang-Mills instantons on ALE gravitational instantons, Math. Ann., 288 (1990), 263-307.
10) S. Mukai, Duality between D(X) and D(X), with applications to Picard sheaves, Nagoya Math. J., 81 (1981), 153-175.
11) H. Nakajima, Moduli spaces of anti-self-dual connections on ALE gravitational instantons, Invent. Math., 102 (1990), 267-303.
12) T. Nitta, Yang-Mills connections on quaternionic Kähler quotients, Proc. Japan Acad., 66 (1990), 245-247.
13) H. Schenk, On a generalised Fourier transform of instantons over flat tori, Comm. Math. Phys., 116 (1988), 177-183.
14) A. F. Swann, Aspects symplectique de la géométrie quaternionique, C. R. Acad. Sci. Paris, 308 (1989), 225-228.

Right : [1] A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987.
[2] P. J. Braam and P. van Baal, Nahm's transformation for instantons, Comm. Math. Phys., 122 (1989), 267-280.
[3] D. S. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, MSRI Publ., 1, Springer-Verlag, 1984.
[4] K. Galicki and H. B. Lawson, Quaternionic reduction and quaternionic orbifolds,Math. Ann., 282 (1988), 1-21.
[5] N. J. Hitchin, Metrics on moduli spaces, in Proceedings of the Lefschez Centennial Conference (Contemporary Math, 58, Part I), A. M. S., Providence, R. I., 1986.
[6] N. J. Hitchin, A. Karlhede, U. Lindström and M. Rocek, Hyperkähler metrics and supersymmetry, Comm. Math. Phys., 108 (1987), 535-589.
[7] M. Itoh, Gauge fields and quaternion structure, Kodai Math. J., 11 (1988), 344-360.
[8] P. B. Kronheimer, The construction of ALE spaces as hyper-kähler quotients, J. Diff. Geom., 29 (1989), 665-683.
[9] P. B. Kronheimer and H. Nakajima, Yang-Mills instantons on ALE gravitational instantons, Math. Ann., 288 (1990), 263-307.
[10] S. Mukai, Duality between D(X) and D(X), with applications to Picard sheaves, Nagoya Math. J., 81 (1981), 153-175.
[11] H. Nakajima, Moduli spaces of anti-self-dual connections on ALE gravitational instantons, Invent. Math., 102 (1990), 267-303.
[12] T. Nitta, Yang-Mills connections on quaternionic Kähler quotients, Proc. Japan Acad., 66 (1990), 245-247.
[13] H. Schenk, On a generalised Fourier transform of instantons over flat tori, Comm. Math. Phys., 116 (1988), 177-183.
[14] A. F. Swann, Aspects symplectique de la géométrie quaternionique, C. R. Acad. Sci. Paris, 308 (1989), 225-228.

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