Skip to main content

Advertisement

Log in

Moduli of representations of the fundamental group of a smooth projective variety. II

  • Published:
Publications Mathématiques de l'Institut des Hautes Études Scientifiques Aims and scope Submit manuscript

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.

References

  1. M. Artin, Algebraic approximation of structures over complete local rings,Publ. Math. I.H.E.S.,36 (1969), 23–58.

    MATH  MathSciNet  Google Scholar 

  2. J. Bernstein, Course onD-modules, Harvard, 1983–1984.

  3. A. Borel, J. Tits, Eléments unipotents et sous-groupes paraboliques de groupes réductifs I,Invent. Math.,12 (1971), 95–104.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  5. P. Deligne, Equations différentielles à points singuliers réguliers,Lect. Notes in Math.,163, Springer, New York (1970).

    MATH  Google Scholar 

  6. P. Deligne, Letter, 1989.

  7. P. Deligne andJ. Milne, Tannakian categories, inLect. Notes in Math.,900, Springer (1982), 101–228.

    Article  MathSciNet  Google Scholar 

  8. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. D. Gieseker, On the moduli of vector bundles on an algebraic surface,Ann. of Math.,106 (1977), 45–60.

    Article  MathSciNet  Google Scholar 

  12. W. Goldman andJ. Millson,The deformation theory of representations of fundamental groups of compact Kähler manifolds, University of Maryland preprint (0000).

  13. A. Grothendieck,Eléments de géométrie algébrique, Several volumes inPubl. Math. I.H.E.S.

  14. A. Grothendieck, Techniques de construction et théorèmes d’existence en géométrie algébrique, IV : Les schémas de Hilbert,Séminaire Bourbaki, Exposé 221, volume 1960–1961.

  15. A. Grothendieck, Crystals and the De Rham cohomology of schemes,Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam (1968).

    Google Scholar 

  16. V. Guillemin, S. Sternberg, Birational equivalence in symplectic geometry,Invent. Math.,97 (1989), 485–522.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. Hartshorne,Algebraic Geometry, Springer, New York (1977).

    MATH  Google Scholar 

  18. 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 

  19. N. J. Hitchin, Stable bundles and integrable systems,Duke Math. J.,54 (1987), 91–114.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. Kempf, L. Ness, On the lengths of vectors in representation spaces,Lect. Notes in Math.,732, Springer, Heidelberg (1982), 233–243.

    Google Scholar 

  21. F. Kirwan,Cohomology of Quotients in Symplectic and Algebraic Geometry, Princeton Univ. Press, Princeton (1984).

    MATH  Google Scholar 

  22. J. Le Potier, Fibrés de Higgs et systèmes locaux,Séminaire Bourbaki 737 (1991).

  23. D. Luna, Slices étales,Bull. Soc. Math. France, Mémoire 33 (1973), 81–105.

    MATH  Google Scholar 

  24. M. Maruyama, Moduli of stable sheaves, I:J. Math. Kyoto Univ.,17-1 (1977), 91–126; II:Ibid.,18-3 (1978), 557–614.

    MathSciNet  Google Scholar 

  25. M. Maruyama, On boundedness of families of torsion free sheaves,J. Math. Kyoto Univ.,21-4 (1981), 673–701.

    MathSciNet  Google Scholar 

  26. Matsushima, See reference inGeometric Invariant Theory.

  27. 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 

  28. 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 

  29. V. V. Morozov, Proof of the regularity theorem (Russian),Usp. M. Nauk.,XI (1956), 191–194.

    Google Scholar 

  30. D. Mumford,Geometric Invariant Theory, Springer Verlag, New York (1965).

    MATH  Google Scholar 

  31. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  33. N. Nitsure,Moduli of semi-stable logarithmic connections, preprint (1991).

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

    MATH  MathSciNet  Google Scholar 

  35. W. M. Oxbury,Spectral curves of vector bundle endomorphisms, preprint, Kyoto University (1988).

  36. W. Rudin,Real and Complex Analysis, Mac Graw-Hill, New York (1974).

    MATH  Google Scholar 

  37. N. Saavedra Rivano, Catégories tannakiennes,Lect. Notes in Math.,265, Springer (1972).

  38. C. S. Seshadri, Space of unitary vector bundles on a compact Riemann surface,Ann. of Math.,85 (1967), 303–336.

    Article  MathSciNet  Google Scholar 

  39. C. S. Seshadri, Mumford’s conjecture for GL(2) and applications,Bombay Colloquium, Oxford University Press (1968), 347–371.

  40. C. Simpson, Yang-Mills theory and uniformization,Lett. Math. Phys.,14 (1987), 371–377.

    Article  MATH  MathSciNet  Google Scholar 

  41. C. 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 

  42. C. Simpson, Nonabelian Hodge theory,International Congress of Mathematicians, Kyoto 1990, Proceedings, Springer, Tokyo (1991), 747–756.

    Google Scholar 

  43. C. Simpson, A lower bound for the monodromy of ordinary differential equations,Analytic and Algebraic Geometry, Tokyo 1990, Proceedings, Springer, Tokyo (1991), 198–230.

    Google Scholar 

  44. C. Simpson, Higgs bundles and local systems,Publ. Math. I.H.E.S.,75 (1992), 5–95.

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  46. 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 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Simpson, C.T. Moduli of representations of the fundamental group of a smooth projective variety. II. Publications Mathématiques de L’Institut des Hautes Scientifiques 80, 5–79 (1994). https://doi.org/10.1007/BF02698895

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02698895

Keywords

Navigation