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8 - Morse theory and stable pairs

Published online by Cambridge University Press:  05 November 2011

By
Richard A. Wentworth  and
Graeme Wilkin
Edited by
Roger Bielawski ,
Kevin Houston  and
Martin Speight
Richard A. Wentworth
Affiliation:
Department of Mathematics, University of Maryland
Graeme Wilkin
Affiliation:
Department of Mathematics, University of Colorado
Roger Bielawski
Affiliation:
University of Leeds
Kevin Houston
Affiliation:
University of Leeds
Martin Speight
Affiliation:
University of Leeds
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Information
Variational Problems in Differential Geometry , pp. 142 - 181
Publisher: Cambridge University Press
Print publication year: 2011

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References

[1] M. F., Atiyah and R., Bott. The Yang-Mills equations over Riemann surfaces. Philos. Trans. Roy. Soc. London Ser. A, 308 (1983), 523–615.Google Scholar
[2] R., Bott. Nondegenerate critical manifolds. Ann. of Math., 60 (1954), no. 2, 248–261.Google Scholar
[3] S., Bradlow. Special metrics and stability for holomorphic bundles with global sections. J. Differential Geom. 33 (1991), no. 1, 169–213.Google Scholar
[4] S., Bradlow and G.D., Daskalopoulos. Moduli of stable pairs for holomorphic bundles over Riemann surfaces. Internat. J. Math. 2 (1991), no. 5, 477–513.Google Scholar
[5] S., Bradlow, G.D., Daskalopoulos, and R.A., Wentworth. Birational equivalences of vortex moduli. Topology 35 (1996), no. 3, 731–748.Google Scholar
[6] G.D., Daskalopoulos. The topology of the space of stable bundles on a compact Riemann surface. J. Differential Geom. 36 (1992), no. 3, 699–746.Google Scholar
[7] G.D., Daskalopoulos and R.A., Wentworth. Convergence properties of the Yang-Mills flow on Käahler surfaces. J. Reine Angew. Math. 575 (2004), 69–99.Google Scholar
[8] G.D., Daskalopoulos, R.A., Wentworth, J., Weitsman, and G., Wilkin. Morse theory and hyperkäahler Kirwan surjectivity for Higgs bundles. J. Differential Geom. 87 (2011), no. 1, 81–116.Google Scholar
[9] S. K., Donaldson. Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. London Math. Soc. (3) 50(1) (1985), 1–26.Google Scholar
[10] M.-C., Hong. Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric. Ann. Global Anal. Geom. 20(1) (2001), 23–46.Google Scholar
[11] M.-C., Hong and G., Tian. Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections. Math. Ann. 330(3) (2004), 441–472.Google Scholar
[12] A., King and P., Newstead. Moduli of Brill-Noether pairs on algebraic curves. Internat. J. Math. 6 (1995), no. 5, 733–748.Google Scholar
[13] F. C., Kirwan. “Cohomology of quotients in symplectic and algebraic geometry”, volume 31 of Mathematical Notes. Princeton University Press, Princeton, NJ, 1984.Google Scholar
[14] S., Kobayashi. “Differential geometry of complex vector bundles”, volume 15 of Publications of the Mathematical Society of Japan. Princeton University Press, Princeton, NJ, 1987., Kano Memorial Lectures, 5.Google Scholar
[15] J. Le, Potier. Systèmes cohérents et structures de niveau. Astérisque No. 214 (1993), 143 pp.
[16] I. G., Macdonald. Symmetric products of an algebraic curve. Topology 1 (1962), 319–343.Google Scholar
[17] J., Råde. On the Yang-Mills heat equation in two and three dimensions. J. Reine Angew. Math. 431 (1992), 123–163.Google Scholar
[18] N., Raghavendra and P., Vishwanath. Moduli of pairs and generalized theta divisors. Tohoku Math. J. (2) 46 (1994), no. 3, 321–340.Google Scholar
[19] L., Simon. Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. of Math. (2) 118(3) (1983), 525–571.Google Scholar
[20] M., Thaddeus. Stable pairs, linear systems and the Verlinde formula. Invent. Math. 117, no. 2 (1994), 317–353.Google Scholar
[21] G., Wilkin. Morse theory for the space of Higgs bundles. Comm. Anal.Geom. 16, no. 2 (2008), 283–332.Google Scholar

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