Communications in Mathematical Physics

, Volume 125, Issue 2, pp 355–367 | Cite as

The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle

  • Jean-Michel Bismut
  • Eric Vasserot


The purpose of this paper is to establish an asymptotic fomula for the Ray-Singer analytic torsion associated with increasing powers of a given positive line bundle.


Neural Network Statistical Physic Complex System High Power Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B1]
    Bismut, J.M.: Demailly's asymptotic Morse inequalities: a heat equation proof. J. Funct. Anal.72, 263–278 (1987)Google Scholar
  2. [B2]
    Bismut, J.M.: Superconnection currents and complex immersions. Invent. Math. (to appear)Google Scholar
  3. [BGS1]
    Bismut, J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott-Chern forms. Commun. Math. Phys.115, 79–126 (1988)Google Scholar
  4. [BGS2]
    Bismut, J.M., Gillet, H., Soulé, C.: Analytic torsion and holomorphic determinant bundles. III. Quillen metrics on holomorphic determinants. Commun. Math. Phys.115, 301–351 (1988)Google Scholar
  5. [BV]
    Bismut, J.M., Vasserot, E.: Comportement asymptotique de la torsion analytique associée aux puissances d'un fibré en droites positif. C.-R. Acad. Sci. Paris307, 779–781 (1988)Google Scholar
  6. [Bo]
    Bost, J.B.: To appearGoogle Scholar
  7. [D1]
    Demailly, J.P.: Champs magnétiques et inégalités de Morse pour lad″ cohomologie. Ann. Inst. Fourier35, 189–229 (1985)Google Scholar
  8. [D2]
    Demailly, J.P.: Sur l'identité de Bochner-Kodairo-Nakano en géométrie Hermitienne. Séminaire Dolbeault-Lelong-Skoda. Lecture Notes in Math., vol. 1198, pp. 88–97. Berlin, Heidelberg, New York: Springer 1986Google Scholar
  9. [F]
    Faltings, G.: Calculus on arithmetic surfaces. Ann. Math.119, 387–424 (1984)Google Scholar
  10. [Ge]
    Getzler, E.: An analogue of Demailly's inequality for strictly pseudoconvex manifolds. J. Diff. Geom.29, 231–244 (1989)Google Scholar
  11. [GS]
    Gillet, H., Soulé, C.: Amplitude arithmétique. C.-R. Acad. Sc. Paris307, 887–890 (1988)Google Scholar
  12. [GrH]
    Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978Google Scholar
  13. [Gre]
    Greiner, P.: An asymptotic expansion for the heat equation. Arch. Ration. Mech. Anal.41, 163–218 (1971)Google Scholar
  14. [Q]
    Quillen, D.: Determinants of Cauchy-Riemann operators. Funct. Anal. Appl.44, 31–34 (1985)Google Scholar
  15. [RS]
    Ray, D.B., Singer, I.M.: Analytic torsion for complex manifolds. Ann. Math.98, 154–177 (1973)Google Scholar
  16. [S]
    Seeley, R.T.: Complex powers of an elliptic operator. Proc. Symp. Pure Math., Vol.10, pp. 288–307. Providence, R.I: Am. Math. Soc. 1967Google Scholar
  17. [V]
    Vojta, P.: An extension of the Thue-Siegel-Dyson-Gel'fond theorem. Preprint 1989Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Jean-Michel Bismut
    • 1
  • Eric Vasserot
    • 2
  1. 1.Département de MathématiqueUniversité Paris-SudOrsayFrance
  2. 2.Ecole Normale SupérieureParisFrance

Personalised recommendations