Fibrés stables et métriques d'Hermite-Einstein

Christophe Margerin

Séminaire Bourbaki (1986-1987)

  • Volume: 29, page 263-283
  • ISSN: 0303-1179

How to cite


Margerin, Christophe. "Fibrés stables et métriques d'Hermite-Einstein." Séminaire Bourbaki 29 (1986-1987): 263-283. <>.

author = {Margerin, Christophe},
journal = {Séminaire Bourbaki},
keywords = {stable bundles; Yang-Mills theory; Kähler manifold; holomorphic vector bundle; Hermitian-Einstein connection},
language = {fre},
pages = {263-283},
publisher = {Société Mathématique de France},
title = {Fibrés stables et métriques d'Hermite-Einstein},
url = {},
volume = {29},
year = {1986-1987},

AU - Margerin, Christophe
TI - Fibrés stables et métriques d'Hermite-Einstein
JO - Séminaire Bourbaki
PY - 1986-1987
PB - Société Mathématique de France
VL - 29
SP - 263
EP - 283
LA - fre
KW - stable bundles; Yang-Mills theory; Kähler manifold; holomorphic vector bundle; Hermitian-Einstein connection
UR -
ER -


  1. [A-B] M.F. Atiyah- R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser.A308 (1982), 524-615. Zbl0509.14014MR702806
  2. [Bi] E. Bishop, Conditions for the analyticity of certain sets, Michigan Math.J. (1964), 289-304. Zbl0143.30302MR168801
  3. [Bo] F. Bogomolov, Holomorphic tensors and vector bundles, Izvestia USSR42 (1978),1227-1287. Zbl0439.14002MR522939
  4. [D1] S.K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom., 18 (1983), 269-277. Zbl0504.49027MR710055
  5. [D2] S.K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundlesProc. London Math. Soc. (3) 50 (1985), 1-26. Zbl0529.53018MR765366
  6. [D3] S.K. Donaldson, Inimité determinants - Stable bundles and curvature, Preprint (Oxford-England). 
  7. [G-T] D. Gilbarg et N.S. Trudinger, Elliptic Partial Differential equations of second order, Springer1977. Zbl0361.35003MR473443
  8. [Ham] R.S. Hamilton, Harmonic Maps of manifolds with boundary, Lecture Notes in Mathematics471 (Springer1975). Zbl0308.35003MR482822
  9. [Hi] N.J. Hitchin, The self duality equations on a Riemann surface, à paraître in Proc. London Math. Soc. Zbl0634.53045
  10. [Ko] S. Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A. Math. Sci.58 (1982), 158-162. Zbl0546.53041MR664562
  11. [Lü1] M. Lubke, Chernklassen von Hermite-Einstein-Vektorbündeln, Math. Ann.260 (1982), 133-141. Zbl0471.53043MR664372
  12. [Lü2] M. Lubke, Stability of Einstein-Hermitian Vector bundles, Manuscripta Math.42 (1983), 245-257. Zbl0558.53037MR701206
  13. [M-R1] R.B. Mehta, A. Ramanathan, Semi-stable sheaves on projective varieties and their restriction to curves, Math. Ann.258 (1982), 213-224. Zbl0473.14001
  14. [M-R2] R.B. Mehta, A. Ramanathan, Restriction of stable sheaves and representations of the fundamental group, Invent. Math.77, 163-172 (1984). Zbl0525.55012MR751136
  15. [N-S] M.S. Narasimhan, C.S. Seshadri, Stable and unitary vector bundles on compact Riemann surfaces, Ann. of Math.82 (1965), 540-567. Zbl0171.04803MR184252
  16. [O-S-S] C. Okonek, M. Schneider, H. Spindler, Vector bundles on complex projective spaces, Birkhäuser (1980). Zbl0438.32016MR561910
  17. [ s.g.a] F. Campana, le théorème sur les limites d'ensembles analytiques de E. Bishop, le Séminaire de Géométrie Analytique, Publication de l'Institut Elie Cartan n°5, Janvier 1982. MR725695
  18. [ s.g.a] C. Sabbah, Application du théorème de Bishop à l'espace des cycles, Séminaire de Géométrie Analytique, Publication de l'Institut Elie Cartan n°5, Janvier 1982. 
  19. [U] K.K. Uhlenbeck, Connections with Lp bounds on curvature, Comm. Math. Phys.83 (1982), 31-42. Zbl0499.58019MR648356
  20. [U-Y] K.K. Uhlenbeck et S.T. Yau, On the existence of Hermitian-Yang-Mills connections in stable Vector Bundles, Preprint, (à paraître dans Communication Pure and Applied Math). Zbl0615.58045MR861491

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