Duke Mathematical Journal

Infinite determinants, stable bundles and curvature

S. K. Donaldson

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Article information

Source
Duke Math. J. Volume 54, Number 1 (1987), 231-247.

Dates
First available: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077305512

Mathematical Reviews number (MathSciNet)
MR885784

Zentralblatt MATH identifier
0627.53052

Digital Object Identifier
doi:10.1215/S0012-7094-87-05414-7

Subjects
Primary: 32L15: Bundle convexity [See also 32F10]
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.

Citation

Donaldson, S. K. Infinite determinants, stable bundles and curvature. Duke Mathematical Journal 54 (1987), no. 1, 231--247. doi:10.1215/S0012-7094-87-05414-7. http://projecteuclid.org/euclid.dmj/1077305512.


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References

  • [1] M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 524–615.
  • [2] J.-M. Bismut and D. S. Freed, The analysis of elliptic families, I, II, to appear in Commun. Math. Phys.
  • [3] S. K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. (3) 50 (1985), no. 1, 1–26.
  • [4] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983.
  • [5] H. Gillet and C. Soulé, Classes caractéristiques en théorie d'Arakelov, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 9, 439–442.
  • [6] Yu. I. Manin, New dimensions in geometry, Workshop Bonn 1984 (Bonn, 1984), Lecture Notes in Math., vol. IIII, Springer, Berlin, 1985, pp. 59–101.
  • [7] V. B. Mehta and A. Ramanathan, Restriction of stable sheaves and representations of the fundamental group, Invent. Math. 77 (1984), no. 1, 163–172.
  • [8] M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567.
  • [9] D. B. Ray and I. M. Singer, Analytic Torsion for complex manifolds, Ann. of Math. (2) 98 (1973), 154–177.
  • [10] K. K. Uhlenbeck and S. T. Yau, The existence of Hermitian Yang-Mills connections on stable bundles over Kahler manifolds, preprint.