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Geometry of anti-self-dual connections and Kuranishi map
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1988 Volume 40 Issue 1 Pages 9-33
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- Published: 1988 Received: June 06, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. Ahlfors, Curvature properties of Teichmüller's space, J. Analyse Math., 9 (1961), 161-176.
2) M. F. Atiyah, Geometry of Yang-Mills fields, Accademia Nazionale dei lincei scuola superiore, Pisa, 1979.
3) M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London, A. 362 (1978), 425-461.
4) M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London, A. 308 (1982), 523-615.
5) W. Barth, Moduli of vector bundles on the projective planes, Invent. Math., 42 (1977), 63-91.
6) M. Berger, Sur les variétés d'Einstein compactes, C. R. IIIe Reunion Math., Expression latine, Namur, 1965, pp. 35-55.
7) S. K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom., 18 (1983), 269-277.
8) S. K. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geom., 18(1983), 279-315.
9) S. K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc., (3) 50 (1985), 1-26.
10) S. K. Donaldson, Connections, cohomology and the intersection forms of 4-manifolds, J. Differential Geom., 24 (1986), 275-341.
11) D. S. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, Springer, 1984.
12) M. Itoh, On Kaehler metrics on a compact homogeneous complex manifold, Tohoku Math. J., 28(1976), 1-5.
13) M. Itoh, Self-dual Yang-Mills equations and Taubes' theorem, Tsukuba J. Math., 8 (1984), 1-29.
14) M. Itoh, The moduli space of Yang-Mills connections over a Kähler surface is a complex manifold, Osaka J. Math., 22 (1985), 845-862.
15) M. Itoh, Yang-Mills connections over a complex surface and harmonic curvature, Compositio Mathematica, 62 (1987), 95-106.
16) S. Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A. Math. Sci., 58 (1982), 158-162.
17) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, Interscience, 1963.
18) K. Kodaira and J. Morrow, Complex Manifolds, Rinehart, 1971.
19) N. Koiso, Einstein metrics and complex structures, Invent. Math., 73 (1983), 71-106.
20) M. Kuranishi, New proof for the existence of locally complete families of complex structures, in Proceedings of the Conference on Complex Analysis (ed. A. Aeppli et al.), Minneapolis, Springer, 1965, pp. 142-154.
21) M. Lübke, Stability of Einstein-Hermitian vector bundles, Manuscripta Math., 42 (1983), 245-257.
22) M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-567.
23) P.E. Newstead, Rationality of moduli space of stable bundles, Math. Ann., 215 (1975), 251-268 (Cor. Ann. of Math., 249 (1980), 281-282).
24) C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective spaces, Birkhäuser, Boston, 1980.
25) G. Schumacher, On the geometry of moduli spaces, Manuscripta Math., 50 (1985), 229-267.
Right : [1] L. Ahlfors, Curvature properties of Teichmüller's space, J. Analyse Math., 9 (1961), 161-176.
[2] M. F. Atiyah, Geometry of Yang-Mills fields, Accademia Nazionale dei lincei scuola superiore, Pisa, 1979.
[3] M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London, A. 362 (1978), 425-461.
[4] M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London, A. 308 (1982), 523-615.
[5] W. Barth, Moduli of vector bundles on the projective planes, Invent. Math., 42 (1977), 63-91.
[6] M. Berger, Sur les variétés d'Einstein compactes, C. R. IIIe Reunion Math., Expression latine, Namur, 1965, pp. 35-55.
[7] S. K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom., 18 (1983), 269-277.
[8] S. K. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geom., 18 (1983), 279-315.
[9] S. K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc., (3) 50 (1985), 1-26.
[10] S. K. Donaldson, Connections, cohomology and the intersection forms of 4-manifolds, J. Differential Geom., 24 (1986), 275-341.
[11] D. S. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, Springer, 1984.
[12] M. Itoh, On Kaehler metrics on a compact homogeneous complex manifold, Tôhoku Math. J., 28 (1976), 1-5.
[13] M. Itoh, Self-dual Yang-Mills equations and Taubes' theorem, Tsukuba J. Math., 8 (1984), 1-29.
[14] M. Itoh, The moduli space of Yang-Mills connections over a Kähler surface is a complex manifold, Osaka J. Math., 22 (1985), 845-862.
[15] M. Itoh, Yang-Mills connections over a complex surface and harmonic curvature, Compositio Mathematica, 62 (1987), 95-106.
[16] S. Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A. Math. Sci., 58 (1982), 158-162.
[17] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, Interscience, 1963.
[18] K. Kodaira and J. Morrow, Complex Manifolds, Rinehart, 1971.
[19] N. Koiso, Einstein metrics and complex structures, Invent. Math., 73 (1983), 71-106.
[20] M. Kuranishi, New proof for the existence of locally complete families of complex structures, in Proceedings of the Conference on Complex Analysis (ed. A. Aeppli et al.), Minneapolis, Springer, 1965, pp. 142-154.
[21] M. Lübke, Stability of Einstein-Hermitian vector bundles, Manuscripta Math., 42 (1983), 245-257.
[22] M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-567.
[23] P. E. Newstead, Rationality of moduli space of stable bundles, Math. Ann., 215 (1975), 251-268 (Cor. Math. Ann., 249 (1980), 281-282).
[24] C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective spaces, Birkhäuser, Boston, 1980.
[25] G. Schumacher, On the geometry of moduli spaces, Manuscripta Math., 50 (1985), 229-267.
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