The topology of the space of stable bundles on a compact Riemann surface
Tóm tắt
Từ khóa
Tài liệu tham khảo
[9] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978.
[1] M. F. Atiyah and R. Bott, Yang-Mills equations on Riemann surfaces, Philos. Trans. Roy. Soc. London A 308 (1982) 523-615.
[3] S. B. Bradlow, Vortices on Kahler manifolds, Ph.D.thesis, Chicago, 1988.
[4] G. D. Daskalopoulos and K. K. Uhlenbeck, in preparation.
[5] S. K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Differential 18 (1983) 269-277.
[6] S. K. Donaldson, Anti self dual connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985) 1-26.
[7] S. K. Donaldson, Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987) 231-247.
[8] D. S. Freed and K. K. Uhlenbeck, Instantons and four manifolds, Math. Sci. Res. Inst. Publ. Vol. 1, Springer, Berlin, 1984.
[10] V. Guillemin and A. Pollack, Differential topology, Prentice-Hall, Englewood Cliffs, NJ, 1974.
[11] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982) 515-538.
[12] R. S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Math., Vol. 471, Springer, Berlin, 1975.
[13] G. Harder and M. S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann. 212 (1975) 215-248.
[14] N. Hitchin, The self duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1982) 59-126.
[16] F. C. Kirwan, Sur la cohomologie des espaces quotients, C. R. Acad. Sci. Paris Ser. I 295 (1982) 261-264.
[17] F. C. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Math. Notes, No. 31, Princeton University Press, Princeton, NJ, 1984.
[18] F. C. Kirwan, On the homology of compactifications of moduli spaces of vector bundles over a Riemann surface, Proc. London Math. Soc. (3) 53 (1986) 237-266.
[19] F. C. Kirwan, privatecommunication.
[21] J. Milnor, Morse theory, Annals of Math. Studies, No. 51, Princeton University Press, Princeton, NJ, 1975.
[22] D. Mumford, Geometric invariant theory, Springer, Berlin and New York, 1965. (2nd ed., D. Mumford and J. Fogarty, Springer, Berlin, 1982.)
[23] M. S. Narasimhan and R. Ramanan, Moduli of vector bundles on a compact Riemann surface, Ann. of Math. (2) 89 (1969) 14-51.
[24] L. Ness, A stratification of the null cone via the moment map, Amer. J. Math. 106 (1984) 1281-1329.
[25] C. Okonek, M. Schneider and H. Spindler, Vectorbundles on complex projectivespaces, Progr. in Math., Vol. 3, Birkhauser, Boston, 1980.
[27] R. S. Palais, Foundations of global non-linear analysis, Benjamin, New York, 1968.
[28] C. S. Seshadri, Space of unitary vectorbundles on a compact Riemann surface, Ann. of Math. (2) 85 (1967) 303-336.
[29] S. S. Shatz, The decomposition and specialization of algebraic families of vector bundles, Compositio Math. 35 (1977) 163-187.
[30] C. Simpson, Systems ofHodge bundles and uniformization, Ph.D. thesis, Harvard, 1987.
[31] S. Smale, Morse theory and a nonlinear generalization of the Dirichlet problem, Ann. of Math. (2) 80 (1964).
[33] K. K. Uhlenbeck, Apriori estimates for Yang-Mills, preprint.