Moduli of representations of the fundamental group of a smooth projective variety I

Carlos T. Simpson

Publications Mathématiques de l'IHÉS (1994)

  • Volume: 79, page 47-129
  • ISSN: 0073-8301

How to cite


Simpson, Carlos T.. "Moduli of representations of the fundamental group of a smooth projective variety I." Publications Mathématiques de l'IHÉS 79 (1994): 47-129. <>.

author = {Simpson, Carlos T.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {representation space; moduli space; corepresentation; geometric invariant theory; Hilbert scheme; good quotient; fine moduli spaces},
language = {eng},
pages = {47-129},
publisher = {Institut des Hautes Études Scientifiques},
title = {Moduli of representations of the fundamental group of a smooth projective variety I},
url = {},
volume = {79},
year = {1994},

AU - Simpson, Carlos T.
TI - Moduli of representations of the fundamental group of a smooth projective variety I
JO - Publications Mathématiques de l'IHÉS
PY - 1994
PB - Institut des Hautes Études Scientifiques
VL - 79
SP - 47
EP - 129
LA - eng
KW - representation space; moduli space; corepresentation; geometric invariant theory; Hilbert scheme; good quotient; fine moduli spaces
UR -
ER -


  1. [Ar] M. ARTIN, Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S., 36 (1969), 23-58. Zbl0181.48802MR42 #3087
  2. [Be] J. BERNSTEIN, Course on D-modules, Harvard, 1983-1984. 
  3. [BT] A. BOREL, J. TITS, Eléments unipotents et sous-groupes paraboliques de groupes réductifs I, Invent. Math., 12 (1971), 95-104. Zbl0238.20055MR45 #3419
  4. [Co] K. CORLETTE, Flat G-bundles with canonical metrics, J. Diff. Geom., 28 (1988), 361-382. Zbl0676.58007MR89k:58066
  5. [De1] P. DELIGNE, Equations différentielles à points singuliers réguliers, Lect. Notes in Math., 163, Springer, New York (1970). Zbl0244.14004MR54 #5232
  6. [De2] P. DELIGNE, Letter. 
  7. [DM] P. DELIGNE and J. MILNE, Tannakian categories, In Lect. Notes in Math., 900, Springer (1982), 101-228. Zbl0477.14004MR84m:14046
  8. [Do1] 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. Zbl0529.53018MR86h:58038
  9. [Do2] S. K. DONALDSON, Infinite determinants, stable bundles, and curvature, Duke Math. J., 54 (1987), 231-247. Zbl0627.53052MR88g:32046
  10. [Do3] S. K. DONALDSON, Twisted harmonic maps and self-duality equations, Proc. London Math. Soc., 55 (1987), 127-131. Zbl0634.53046MR88g:58040
  11. [Gi] D. GIESEKER, On the moduli of vector bundles on an algebraic surface, Ann. of Math., 106 (1977), 45-60. Zbl0381.14003MR81h:14014
  12. [GM] W. GOLDMAN and J. MILLSON, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Publ. Math. I.H.E.S., 67 (1988), 43-96. Zbl0678.53059MR90b:32041
  13. [Gr1] A. GROTHENDIECK, Eléments de géométrie algébrique, Several volumes in Publ. Math. I.H.E.S. Zbl0203.23301
  14. [Gr2] A. GROTHENDIECK, Techniques de construction et théorèmes d'existence en géométrie algébrique, IV : Les schémas de Hilbert, Sém. Bourbaki, Exposé 221, volume 1960-1961. Zbl0236.14003
  15. [Gr3] A. GROTHENDIECK, Crystals and the De Rham cohomology of schemes, Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam (1968). Zbl0215.37102MR42 #4558
  16. [GS] V. Guillemin, S. Sternberg, Birational equivalence in symplectic geometry, Invent. Math., 97 (1989), 485-522. Zbl0683.53033MR90f:58060
  17. [Ha] R. HARTSHORNE, Algebraic Geometry, Springer, New York (1977). Zbl0367.14001MR57 #3116
  18. [Hi1] N. J. HITCHIN, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 59-126. Zbl0634.53045MR89a:32021
  19. [Hi2] N. J. HITCHIN, Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91-114. Zbl0627.14024MR88i:58068
  20. [KN] G. KEMPF, L. NESS, On the lengths of vectors in representation spaces, Lect. Notes in Math., 732, Springer, Heidelberg (1982), 233-243. Zbl0407.22012MR81i:14032
  21. [Ki] F. KIRWAN, Cohomology of Quotients in Symplectic and Algebraic Geometry, Princeton Univ. Press, Princeton (1984). Zbl0553.14020MR86i:58050
  22. [Le] J. LE POTIER, Fibrés de Higgs et systèmes locaux, Séminaire Bourbaki 737 (1991). Zbl0762.14011MR93e:14012
  23. [Lu] D. LUNA, Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105. Zbl0286.14014MR49 #7269
  24. [Ma1] M. MARUYAMA, Moduli of stable sheaves, I : J. Math. Kyoto Univ., 17-1 (1977), 91-126 ; II : Ibid., 18-3 (1978), 557-614. Zbl0374.14002MR56 #8567
  25. [Ma2] M. MARUYAMA, On boundedness of families of torsion free sheaves, J. Math. Kyoto Univ., 21-4 (1981), 673-701. Zbl0495.14009MR83a:14019
  26. [Mt] MATSUSHIMA, See reference in Geometric Invariant Theory. 
  27. [MR1] V. B. MEHTA and A. RAMANATHAN, Semistable sheaves on projective varieties and their restriction to curves, Math. Ann., 258 (1982), 213-224. Zbl0473.14001MR83f:14013
  28. [MR2] V. B. MEHTA and A. RAMANATHAN, Restriction of stable sheaves and representations of the fundamental group, Invent. Math., 77 (1984), 163-172. Zbl0525.55012MR85m:14026
  29. [Mo] V. V. MOROZOV, Proof of the regularity theorem (Russian), Usp. M. Nauk., XI (1956), 191-194. Zbl0071.25802MR19,527c
  30. [Mu] D. MUMFORD, Geometric Invariant Theory, Springer Verlag, New York (1965). Zbl0147.39304MR35 #5451
  31. [NS] M. S. NARASIMHAN and C. S. SESHADRI, Stable and unitary bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-564. Zbl0171.04803MR32 #1725
  32. [Ni1] N. NITSURE, Moduli space of semistable pairs on a curve, Proc. London Math. Soc., 62 (1991), 275-300. Zbl0733.14005MR92a:14010
  33. [Ni2] N. NITSURE, Moduli of semi-stable logarithmic connections, Jour. Amer. Math. Soc., 6 (1993), 597-610. Zbl0807.14007MR93i:32025
  34. [No] M. V. NORI, On the representations of the fundamental group, Compositio Math., 33 (1976), 29-41. Zbl0337.14016MR54 #5237
  35. [Ox] W. M. OXBURY, Spectral curves of vector bundle endomorphisms, preprint, Kyoto University (1988). 
  36. [Ru] W. RUDIN, Real and Complex Analysis, Mac Graw-Hill, New York (1974). Zbl0278.26001MR49 #8783
  37. [Sa] N. SAAVEDRA RIVANO, Catégories tannakiennes, Lect. Notes in Math., 265 Springer, (1972). Zbl0241.14008MR49 #2769
  38. [Se1] C. S. SESHADRI, Space of unitary vector bundles on a compact Riemann surface, Ann. of Math., 85 (1967), 303-336. Zbl0173.23001MR38 #1693
  39. [Se2] C. S. SESHADRI, Mumford's conjecture for GL(2) and applications, Bombay Colloquium, Oxford University Press (1968), 347-371. Zbl0194.51702MR41 #6858
  40. [Si1] C. SIMPSON, Yang-Mills theory and uniformization, Lett. Math. Phys., 14 (1987), 371-377. Zbl0635.32017MR89a:32034
  41. [Si2] 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. Zbl0669.58008MR90e:58026
  42. [Si3] C. SIMPSON, Nonabelian Hodge theory, International Congress of Mathematicians, Kyoto 1990, Proceedings, Springer, Tokyo (1991), 747-756. Zbl0765.14005MR93c:14010
  43. [Si4] C. SIMPSON, A lower bound for the monodromy of ordinary differential equations, Analytic and Algebraic Geometry, Tokyo 1990, Proceedings, Springer, Tokyo (1991), 198-230. Zbl0813.32020MR95d:32025
  44. [Si5] C. SIMPSON, Higgs bundles and local systems, Publ. Math. I.H.E.S., 75 (1992), 5-95. Zbl0814.32003MR94d:32027
  45. [Uh] K. K. UHLENBECK, Connections with Lp bounds on curvature, Commun. Math. Phys., 83 (1982), 31-42. Zbl0499.58019MR83e:53035
  46. [UY] K. K. UHLENBECK and S. T. YAU, On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure and Appl. Math., 39-S (1986), 257-293. Zbl0615.58045MR88i:58154

Citations in EuDML Documents

  1. Pietro Tortella, Λ-modules and holomorphic Lie algebroid connections
  2. Dimitri Markushevich, Alexander Tikhomirov, Günther Trautmann, Bubble tree compactification of moduli spaces of vector bundles on surfaces
  3. Francesco Bottacin, Atiyah Classes and Closed Forms on Moduli Spaces of Sheaves
  4. Jean-Marc Drézet, Courbes multiples primitives et déformations de courbes lisses
  5. Siegmund Kosarew, Geometric and categorical nonabelian duality in complex geometry
  6. Andreas Laudin, Alexander Schmitt, Recent results on quiver sheaves
  7. Jean-Marc Drézet, Fragmented deformations of primitive multiple curves
  8. V. Balaji, A.J. Parameswaran, Tensor product theorem for Hitchin pairs – An algebraic approach
  9. Joseph Le Potier, Alexander Tikhomirov, Sur le morphisme de Barth
  10. Jarod Alper, Good moduli spaces for Artin stacks

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