Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface

Hiroshi KONNO

doi:10.2969/jmsj/04520253

Hiroshi KONNO

著者情報

ジャーナルフリー

1993 年 45 巻 2 号 p. 253-276

DOI https://doi.org/10.2969/jmsj/04520253

詳細

Published: 1993 Received: 1992/02/05 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A, 308 (1982), 523-615.
2) M. F. Atiyah, N. J, Hitchin and I. M. Singer, Self-duality in four dimensionl Riemannian geometry, Proc. Roy. Soc. London Ser. A, 362 (1978), 425-461.
3) O. Biquard, Fibrés parabolique stables et connexions singulières plates, Bull. Soc. Math. France, 119 (1991), 231-257.
4) H. Boden, Representations of orbifold groups and parabolic bundles, Comment. Math. Helve., 66 (1991), 389-447.
5) S. B. Bradlow, Special metrics and stability for holomorphic bundles with global sections, J. Differential Geom., 33 (1991), 169-213.
6) S. K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom., 18 (1983), 269-277.
7) S. K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable bundles, Proc. London Math. Soc. (3), 50 (1985), 1-26.
8) S. K. Donaldson, Infinite determinants, stable bundles and curvature, Duke Math. J., 54 (1987), 231-247.
9) A. Fujiki, Hyperkähler structure on the moduli space of flat bundles, Lecture Notes in Math., 1468, Springer, 1991, pp. 1-83.
10) M. Furuta and B. Steer, Seifert fibred homology 3-spheres and Yang-Mills equations on Riemann surfaces with marked points, preprint.
11) N. J. Hitchin, The self duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 58-126.
12) N. J. Hitchin, The symplectic geometry of moduli space of connections and geometric quantization, Progr. of Theoret. Phys., Supplement, 102 (1990), 159-174.
13) N. J. Hitchin, A. Karlhede, U. Lindström and M. Rocek, Hyperkähler metrics and supersymmetry, Comm. Math. Phys., 108 (1987), 535-589.
14) R. B. Lockhart and R. C. McOwen, Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 12 (1985), 409-447.
15) V. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann., 248 (1980), 205-239.
16) M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-564.
17) C. T. Simpson, Constructing variation of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc., 1 (1988), 867-918.
18) C. T. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc., 3 (1990), 713-770.
19) K. K. Uhlenbeck and S. T. Yau, On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure Appl. Math., 39-S (1986), 257-293.
20) B. Nasatyr, Oxford thesis.

Right : [1] M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A, 308 (1982), 523-615.
[2] M. F. Atiyah, N. J, Hitchin and I. M. Singer, Self-duality in four dimensionl Riemannian geometry, Proc. Roy. Soc. London Ser. A, 362 (1978), 425-461.
[3] O. Biquard, Fibrés parabolique stables et connexions singulières plates, Bull. Soc. Math. France, 119 (1991), 231-257.
[4] H. Boden, Representations of orbifold groups and parabolic bundles, Comment. Math. Helve., 66 (1991), 389-447.
[5] S. B. Bradlow, Special metrics and stability for holomorphic bundles with global sections, J. Differential Geom., 33 (1991), 169-213.
[6] S. K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom., 18 (1983), 269-277.
[7] S. K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable bundles, Proc. London Math. Soc. (3), 50 (1985), 1-26.
[8] S. K. Donaldson, Infinite determinants, stable bundles and curvature, Duke Math. J., 54 (1987), 231-247.
[9] A. Fujiki, Hyperkähler structure on the moduli space of flat bundles, Lecture Notes in Math., 1468, Springer, 1991, pp. 1-83.
[10] M. Furuta and B. Steer, Seifert fibred homology 3-spheres and Yang-Mills equations on Riemann surfaces with marked points, preprint.
[11] N. J. Hitchin, The self duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 58-126.
[12] N. J. Hitchin, The symplectic geometry of moduli space of connections and geometric quantization, Progr. of Theoret. Phys., Supplement, 102 (1990), 159-174.
[13] N. J. Hitchin, A. Karlhede, U. Lindström and M. Rocek, Hyperkähler metrics and supersymmetry, Comm. Math. Phys., 108 (1987), 535-589.
[14] R. B. Lockhart and R. C. McOwen, Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 12 (1985), 409-447.
[15] V. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann., 248 (1980), 205-239.
[16] M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-564.
[17] C. T. Simpson, Constructing variation of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc., 1 (1988), 867-918.
[18] C. T. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc., 3 (1990), 713-770.
[19] K. K. Uhlenbeck and S. T. Yau, On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure Appl. Math., 39-S (1986), 257-293.
[20] B. Nasatyr, Oxford thesis.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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