Skip to main content
Log in

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. L. V. Ahlfors, An extension of Schwarz’s lemma,Trans. Amer. Math. Soc.,43, no. 3 (1938), 359–364.

    Article  MATH  MathSciNet  Google Scholar 

  2. H. Bass, Groups of integral representation type,Pacific J. of Math.,86 (1980), 15–51.

    MATH  MathSciNet  Google Scholar 

  3. A. Borel andW. Casselman, L2-cohomology of locally symmetric manifolds of finite volume,Duke Math. J.,50 (1983), 625–647.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. A. Carlson andD. Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces,Publ. Math. I.H.E.S.,69 (1989), 173–201.

    MATH  MathSciNet  Google Scholar 

  5. K. Corlette, Flat G-bundles with canonical metrics,J. Diff. Geom.,28 (1988), 361–382.

    MATH  MathSciNet  Google Scholar 

  6. K. Corlette, Rigid representations of Kählerian fundamental groups,J. Diff. Geom.,33 (1991), 239–252.

    MATH  MathSciNet  Google Scholar 

  7. P. Deligne, letter to J.-P. Serre (1968).

  8. P. Deligne, Un théorème de finitude pour la monodromie,Discrete Groups in Geometry and Analysis, Birkhauser (1987), 1–19.

  9. P. Deligne, La conjecture de Weil pour les surfaces K3,Invent. Math.,15 (1972), 206–222.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. Deligne, Theorie de Hodge, II,Publ. Math. I.H.E.S.,40 (1971), 5–58.

    MATH  MathSciNet  Google Scholar 

  11. P. Deligne, Travaux de Shimura,Séminaire Bourbaki, Lect. Notes in Math.,244 (1971), 123–165.

    Article  MathSciNet  Google Scholar 

  12. P. Deligne, P. Griffiths, J. Morgan andD. Sullivan, Real homotopy theory of Kähler manifolds,Invent. Math.,29 (1975), 245–274.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Deligne, J. S. Milne, A. Ogus andK. Shih,Hodge Cycles, Motives, and Shimura Varieties,Lect. Notes in Math.,900 (1982), Heidelberg, Springer.

    MATH  Google Scholar 

  14. K. Diederich andT. Ohsawa, Harmonic mappings and disc bundles over compact Kähler manifolds,Publ. R.I.M.S.,21 (1985), 819–833.

    MATH  MathSciNet  Google Scholar 

  15. P. Dolbeault, Formes différentielles et cohomologie sur une variété analytique complexe, I,Ann. of Math.,64 (1956), 83–130.

    Article  MathSciNet  Google Scholar 

  16. S. K. Donaldson, Anti self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles,Proc. London Math. Soc. (3),50 (1985), 1–26.

    Article  MATH  MathSciNet  Google Scholar 

  17. S. K. Donaldson, Infinite determinants, stable bundles, and curvature,Duke Math. J.,54 (1987), 231–247.

    Article  MATH  MathSciNet  Google Scholar 

  18. S. K. Donaldson, Twisted harmonic maps and self-duality equations,Proc. London Math. Soc.,55 (1987), 127–131.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Eells andJ. H. Sampson, Harmonic mappings of Riemannian manifolds,Amer. J. Math.,86 (1964), 109–160.

    Article  MATH  MathSciNet  Google Scholar 

  20. H. Garland andM. S. Raghunathan, Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups,Ann. of Math.,92 (1970), 279–326.

    Article  MathSciNet  Google Scholar 

  21. W. Goldman andJ. Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds,Publ. Math. I.H.E.S.,67 (1988), 43–96.

    MATH  MathSciNet  Google Scholar 

  22. M. Green andR. Lazarsfeld, Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese, and Beauville,Invent. Math.,90 (1987), 389–407.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Green andR. Lazarsfeld,Higher obstructions to deforming cohomology groups of line bundles, Preprint (1990).

  24. P. Griffiths, Periods of integrals on algebraic manifolds I, II,Amer. J. Math.,90 (1968), III,Publ. Math. I.H.E.S.,38 (1970).

  25. P. Griffiths andJ. Harris,Principles of Algebraic Geometric, John Wiley & Sons (1978).

  26. P. Griffiths andW. Schmid, Locally homogeneous complex manifolds,Acta Math.,123 (1969), 253–302.

    Article  MathSciNet  Google Scholar 

  27. R. Hain, The de Rham homotopy theory of complex algebraic varieties, I, K-Theory,1 (1987), 271–324.

    Article  MATH  MathSciNet  Google Scholar 

  28. S. Helgason,Differential geometry, Lie groups, and symmetric spaces, New York, Academic Press (1978).

    MATH  Google Scholar 

  29. P. W. Higgs, Broken symmetries and the masses of gauge bosons,Phys. Rev. Lett.,13, no. 16 (1964), 508–509.

    Article  MathSciNet  Google Scholar 

  30. N. J. Hitchin, The self-duality equations on a Riemann surface,Proc. London Math. Soc. (3),55 (1987), 59–126.

    Article  MATH  MathSciNet  Google Scholar 

  31. G. Hochschild andG. D. Mostow, On the algebra of representative functions of an analytic group,Amer. J. Math.,83 (1961), 111–136.

    Article  MATH  MathSciNet  Google Scholar 

  32. G. Hochschild, Coverings of pro-affine algebraic groups,Pacific J. Math.,35 (1970), 399–415.

    MATH  MathSciNet  Google Scholar 

  33. P. B. Kronheimer, M. J. Larsen andJ. Scherk, Casson’s invariant and quadratic reciprocity,Topology,30 (1991), 335–338.

    Article  MATH  MathSciNet  Google Scholar 

  34. M. Lubke, Chernklassen von Hermite-Einstein-vektorbundeln,Math. Ann.,260 (1982), 133–141.

    Article  MathSciNet  Google Scholar 

  35. G. A. Margulis, Discrete groups of motions of manifolds of nonpositive curvature,Proc. Inter. Cong. Math. Vancouver (1974), v. 2, 21–34; transl.Amer. Math. Soc. Transl.,109 (1977), 33–45.

    Google Scholar 

  36. V. B. Mehta andA. Ramanathan, Semistable sheaves on projective varieties and their restriction to curves,Math. Ann.,258 (1982), 213–224.

    Article  MATH  MathSciNet  Google Scholar 

  37. V. B. Mehta andA. Ramanathan, Restriction of stable sheaves and representations of the fundamental group,Invent. Math.,77 (1984), 163–172.

    Article  MATH  MathSciNet  Google Scholar 

  38. J. Morgan, The algebraic topology of smooth algebraic varieties,Publ. Math. I.H.E.S.,48 (1978), 137–204; and64 (1985), 185.

    MATH  Google Scholar 

  39. M. S. Narasimhan andC. S. Seshadri, Stable and unitary bundles on a compact Riemann surface,Ann. of Math.,82 (1965), 540–564.

    Article  MathSciNet  Google Scholar 

  40. N. Nitsure, Moduli spaces of semistable pairs on a curve,Proc. London Math. Soc. 62 (1991), 275–300.

    Article  MATH  MathSciNet  Google Scholar 

  41. M. V. Nori, On the representations of the fundamental group,Compositio Math.,33 (1976), 29–41.

    MATH  MathSciNet  Google Scholar 

  42. M. S. Ragunathan, Cohomology of arithmetic subgroups of algebraic groups, I,Ann. of Math.,86 (1967), 409–424; II,Ann. of Math.,87 (1968), 279–304.

    Article  Google Scholar 

  43. N. Saavedra Rivano,Catégories tannakiennes,Lect. Notes in Math.,265, Heidelberg, Springer-Verlag (1972).

    MATH  Google Scholar 

  44. J. H. Sampson, Applications of harmonic maps to Kähler geometry,Contemp. Math.,49 (1986), 125–133.

    MATH  MathSciNet  Google Scholar 

  45. J.-P. Serre,Linear Representations of Finite Groups, New York, Springer-Verlag (1977).

    MATH  Google Scholar 

  46. C. T. Simpson,Systems of Hodge bundles and uniformization, doctoral dissertation, Harvard University (1987).

  47. C. T. Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization,Journal of the A.M.S.,1 (1988), 867–918.

    MATH  MathSciNet  Google Scholar 

  48. C. T. Simpson, Transcendental aspects of the Riemann-Hilbert correspondence,Illinois J. of Math.,34 (1990), 368–391.

    MATH  MathSciNet  Google Scholar 

  49. Y. T. Siu, Complex analyticity of harmonic maps and strong rigidity of complex Kähler manifolds,Ann. of Math.,112 (1980), 73–110.

    Article  MathSciNet  Google Scholar 

  50. T. Tannaka, Über den Dualitätssatz der nichtkommutativen topologischen Gruppen,Tohoku Math. J.,45 (1938), 1–12.

    MATH  Google Scholar 

  51. K. K. Uhlenbeck, Connections with Lp bounds on curvature,Comm. Math. Phys.,83 (1982), 31–42.

    Article  MATH  MathSciNet  Google Scholar 

  52. K. K. Uhlenbeck andS. T. Yau, On the existence of Hermitian-Yang-Mills connections in stable vector bundles,Comm. Pure and Appl. Math.,39-S (1986), 257–293.

    Article  MathSciNet  Google Scholar 

  53. A. Weil,Introduction à l’étude des variétés kähleriennes, Paris, Hermann (1952).

    Google Scholar 

  54. A. Weil, Discrete subgroups of Lie group I,Ann. of Math.,72 (1960), 369–384; II,Ann. of Math.,75 (1962), 578–602; Remarks on the cohomology of groups,Ann. of Math.,80 (1964), 149–157.

    Article  MathSciNet  Google Scholar 

  55. A. Weil,Basic Number Theory, New York, Springer-Verlag (1967).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Prepared with the partial support of NSF grant DMS-8705757.

About this article

Cite this article

Simpson, C.T. Higgs bundles and local systems. Publications Mathématiques de l’Institut des Hautes Scientifiques 75, 5–95 (1992). https://doi.org/10.1007/BF02699491

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02699491

Keywords

Navigation