A lower bound for the size of monodromy of systems of ordinary differential equations

  • Carlos T. Simpson
Conference paper


The material discussed in my talk in Tokyo was mostly contained in the manuscript submitted for the proceedings of ICM-90. The present paper concerns a subject which was not mentioned in Tokyo—I would have discussed it briefly, had there been more time at the end of my talk. Then, the discussion would have been purely conjectural, but in the months after the conference I have been able to give the proof in the rank two case. I apologize for this somewhat tenuous connection between my talk and the material presented here.


Vector Bundle Line Bundle Compact Riemann Surface Holomorphic Section Holomorphic Vector Bundle 
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  1. [1]
    L. Ahlfors, An extension of Schwarz’s lemma. Trans. Amer. Math. Soc. 43 (1938), 359–364.MathSciNetGoogle Scholar
  2. [2]
    M. Atiyah, Vector bundles on elliptic curves. Proc. London Math. Soc. 7 (1957), 424.CrossRefMathSciNetGoogle Scholar
  3. [3]
    T. Aubin, Sur la fonction exponentielle. C. R. Acad. Sci. Paris 270A (1970), 1514–1516.MathSciNetGoogle Scholar
  4. [4]
    K. Corlette, Flat (7-bundles with canonical metrics. J. Diff. Geom. 28 (1988) 361–382.MATHMathSciNetGoogle Scholar
  5. [5]
    P. Deligne, Equations différentielles à points singuliers réguliers. Lect. Notes in Math. 163 Springer, N.Y. (1970).Google Scholar
  6. [6]
    S. Donaldson, Twisted harmonic maps and self-duality equations. Proc. London Math. Soc. 55 (1987), 127–131.CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    D. Gieseker, On the moduli of vector bundles on an algebraic surface. Ann. of Math. 106 (1977), 45–60.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    N. Hitchin, The self-duality equations on a Riemann surface. Proc. London Math. Soc. 55 (1987) 59–126.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    F. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry. Princeton Univ. Press, Princeton (1984).MATHGoogle Scholar
  10. [10]
    R. Langer, The asymptotic solutions of ordinary linear differential equations of the second order with special reference to a turning point. Trans. Amer. Math. Soc. 67 (1949), 461–490.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    M. Maruyama, On the boundedness of families of torsion free sheaves. J. Math. Kyoto Univ. 21-4 (1981), 673–701.MATHMathSciNetGoogle Scholar
  12. [12]
    D. Mumford, Geometric Invariant Theory. Springer Verlag, New York (1965).MATHGoogle Scholar
  13. [13]
    C. Simpson, Harmonic bundles on noncompact curves. J.A.M.S. 3 (1990), 713–770.MATHMathSciNetGoogle Scholar
  14. [14]
    C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety (preprint).Google Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Carlos T. Simpson
    • 1
  1. 1.Princeton UniversityPrincetonUSA

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