Métriques de Quillen et plongements complexes

Jean-Michel Bismut

Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990)

  • page 1-19

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Bismut, Jean-Michel. "Métriques de Quillen et plongements complexes." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-19. <http://eudml.org/doc/111992>.

@article{Bismut1989-1990,
author = {Bismut, Jean-Michel},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {cohomology of a vector bundle; Dolbeault cohomology; Chern class; current; Hermitian holomorphic connection; curvature; Kähler metric; Hodge theory},
language = {fre},
pages = {1-19},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Métriques de Quillen et plongements complexes},
url = {http://eudml.org/doc/111992},
year = {1989-1990},
}

TY - JOUR
AU - Bismut, Jean-Michel
TI - Métriques de Quillen et plongements complexes
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1989-1990
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 19
LA - fre
KW - cohomology of a vector bundle; Dolbeault cohomology; Chern class; current; Hermitian holomorphic connection; curvature; Kähler metric; Hodge theory
UR - http://eudml.org/doc/111992
ER -

References

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  1. [AS] Atiyah, M.F., Singer Lm.: The index of elliptic operators. III Ann. of Math.87, 546-604 (1968). Zbl0164.24301MR236952
  2. [B1] Bismut, J.M.: Superconnection currents and complex immersions. Invent. Math. (1990), 59-113. Zbl0696.58006MR1029391
  3. [B2] Bismut, J.M.: Koszul complexes, harmonic oscillators and the Todd class. J.A.M.S.3, 159-256 (1990). Zbl0702.58071MR1017783
  4. [B3] Bismut, J.M.: The Atiyah-Singer index Theorem: a probabilistic approach. I: The index Theorem. J. Funct. Anal.57, 56- 99 (1984). Zbl0538.58033MR744920
  5. [B4] Bismut, J.M.: Superconnexions, indice local des familles, déterminant de la cohomologie et métriques de Quillen. A paraître. Zbl0755.58009
  6. [BGS1] Bismut, J.M., Gillet, H., Soulé C.: Analytic torsion and holomorphic déterminant bundles. I. Comm. Math. Phys.115, 49-78 (1988). Zbl0651.32017MR929146
  7. [BGS2] Bismut J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles. II. Comm. Math. Phys.115, 79-126 (1988). Zbl0651.32017MR929147
  8. [BGS3] Bismut, J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic déterminant bundles. III. Comm. Math. Phys.115, 301-351 (1988). Zbl0651.32017MR931666
  9. [BGS4] Bismut, J.M., Gillet, H., Soulé, C.: Bott-Chern currents and complex immersions. Duke Math. Journal60, 255-284(1990). Zbl0697.58005MR1047123
  10. [BL1] Bismut, J.M., Lebeau, G.Immersions complexes et métriques de Quillen. C.R. Acad. Sci. Paris Sér. I. Math309, 487-491 (1989). Zbl0681.53034MR1055464
  11. [BL2] Bismut, J.M., Lebeau, G.Complex immersions and Quillen metrics. Preprint Orsay 90-13 (1990). Zbl0784.32010MR1188532
  12. [BoC] Bott, R., Chern S.S.: Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections. Acta Math.114. 71-112 (1968). Zbl0148.31906MR185607
  13. [Ge] Getzler, E.: A short proof of the Atiyah-Singer Index Theorem. Topology25, 111-117 (1986). Zbl0607.58040MR836727
  14. [GS] Gillet, H., Soulé, C.: Analytic torsion and the arithmetic Todd genus. A paraître dans Topology. Zbl0787.14005MR1081932
  15. [GrH] Griffiths, P., Harris, J., Principles of Algebraic Geometry. New-York: Wiley1978. Zbl0836.14001MR507725
  16. [KM] Knudsen, F.F., Mumford, D.: The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "div". Math. Scand.39, 19-55 (1976). Zbl0343.14008MR437541
  17. [[Q1] Quillen, D.: Superconnections and the Chem character. Topology, 24, 89-95 (1985). Zbl0569.58030MR790678
  18. [Q2] Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface. Funct. Anal. Appl.14, 31-34 (1985). Zbl0603.32016
  19. [RS] Ray, D.B., Singer, IM.: Analytic torsion for complex manifolds. Ann.of Math.98, 154-177 (1973). Zbl0267.32014MR383463
  20. [S] Seeley, R.T.: Complex powers of an elliptic operator. Proc. Symp. Pure and Appl. Math. AMS10, 288-307 (1967). Zbl0159.15504MR237943

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