Fibrés de Higgs et systèmes locaux

Le Potier, Joseph

Séminaire Bourbaki : volume 1990/91, exposés 730-744, Astérisque, no. 201-202-203 (1991), Exposé no. 737, 48 p.

[1] M. F. Atiyah et R. Bott. The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London A308 (1982), 523-615. | Zbl | MR

[2] F. A. Bogomolov. Holomorphic tensors and vector bundles on projectives varieties, Math. USSR Izvestija 13 (1979), 499-555. | Zbl

[3] R. Bott and S. S. Chern. Hermitian vector bundles and the equidistribution of the zeros of their holomorphic cross-sections, Acta Mathematica 114 (1968), 71-112. | Zbl | MR

[4] K. Corlette. Flat G-bundles with canonical metrics, J. Diff. Geom. 28 (1988), 361-382. | Zbl | MR

[5] P. Deligne. Equations différentielles à points singuliers réguliers, Lecture Notes in Maths 163 (1970) Springer. | Zbl | MR

[6] S. K. Donaldson. Infinite determinants, stable bundles and curvature, Duke Math. Journal 54.1 (1987), 231-247. | Zbl | MR

[7] 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. | Zbl | MR

[8] S. K. Donaldson. Twisted harmonic maps and self-duality equations, Proc. London Math. Soc 55 (1987), 127-131. | Zbl | MR

[9] S. K. Donaldson. A new proof of a theorem of Narasimhan and Se- shadri, J. Differential Geom. 18 (1983), 269-277. | Zbl | MR

[10] J. Eells et J. H. Sampson. Harmonic mappings of Riemannian manifolds, Amer. J. of Math. 86 (1964), 109-160. | Zbl | MR

[11] H. Flenner. Restrictions of semistable bundles on projective varieties, Comment. Math. Helvetici 59 (1984), 635-650. | Zbl | MR

[12] D. Gieseker. On the moduli of vector bundles on an algebraic surface, Ann. of Math. 106 (1970), 45-60. | Zbl | MR

[13] W. Goldman et J. Millson. The deformation theory of representation of fundamental groups of compact Kähler manifolds, Preprint, University of Maryland. | MR

[14] P. A. Griffiths. Periods of integrals on algebraic manifolds III, Publ. Math. I.H.E.S. 38 (1970), 125-180. | Zbl | MR | Numdam

[15] A. Grothendieck. Techniques de construction et théorèmes d'existence en géométrie algébrique,IV : les schémas de Hilbert. Séminaire Bourbaki, Exposé 221 (1960-61). | Zbl | Numdam

[16] R. S. Hamilton. Harmonic mappings of riemannian manifolds, Lecture Notes in math. 471 (1975) Springer. | Zbl

[17] R. Hartshorne. Algebraic geometry, Springer (1977). | Zbl | MR

[18] A. Hirschowitz. Sur la restriction des faisceaux semi-stables , Ann. Sc. Ec. Norm. Sup. 14 (1980), 199-207. | Zbl | MR | Numdam

[19] N. J. Hitchin. The self-duality equations on a Riemann surface, Proc. London, Math. Soc.(3)55 (1987), 59-126. | Zbl | MR

[20] N. J. Hitchin. Stable bundles and integrable systems, Duke Math. J. 54 (1987), 91-114. | Zbl | MR

[21] M. Lübke. Chern classen von Hermite-Einstein-Vecktorbündeln, Math. Annalen 260 (1982), 133-141 | Zbl | MR

[22] C. Margerin. Fibrés stables et métriques d'Hermite-Einstein, d'après S.K. Donaldson, K.K. Uhlenbeck et S. T. Yau, Séminaire Bourbaki, Exposé 683 (1987). | Zbl | MR | Numdam

[23] M. Maruyama. On boundedness of families of torsion free sheaves, J. Math. Kyoto University 21-4 (1981), 673-701. | Zbl | MR

[24] M. Maruyama. Moduli of stable sheaves, J. Math. Kyoto University, I 17-1 (1977) 91-126; II 18-3 (1978) 557-614. | Zbl

[25] V. B. Mehta et A. Ramanathan. Semistable sheaves on projective varieties and their restriction to curves, Math. Annalen 258 (1982), 213-224 | Zbl | MR

[26] V. B. Mehta et A. Ramanathan. Restriction of stable sheaves and representation of the fundamental group, Invent. math. 77 (1984), 163-172 | Zbl | MR

[27] D. Mumford et J. Fogarty. Geometric invariant theory, Springer (1982). | Zbl | MR

[28] M. S. Narasimhan et C. S. Seshadri. Stable and unitary vector bundles on compact Riemann surfaces, Ann. of maths 82 (1965), 540-567. | Zbl | MR

[29] C. T. Simpson. Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, Journal of the Amer. Math. Soc. 1 (1988), 867-918. | Zbl | MR

[30] C. T. Simpson. Higgs bundles and local systems, Preprint, Princeton University. | MR

[31] C. T. Simpson. Moduli of representations of the fundamental group of a smooth variety, Preprint, Princeton University.

[32] C. T. Simpson. Non abelian Hodge theory, Preprint, Princeton University.

[33] C. T. Simpson. The ubiquity of variations of Hodge structures, Preprint, Princeton University. | MR

[34] C. T. Simpson. Harmonic bundles on non compact curves, Preprint, Princeton University.

[35] C. T. Simpson. Report on twistor space and the mixed Hodge structure on the fundamental group, Preprint, Princeton University.

[36] K. K. Uhlenbeck et 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. | Zbl | MR

[37] A. Weil. Variétés kählériennes, Paris, Hermann (1958). | Zbl | MR