Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bismut, J.M.: Demailly's asymptotic Morse inequalities: a heat equation proof. J. Funct. Anal.72, 263–278 (1987)
Bismut, J.M.: Superconnection currents and complex immersions. Invent. Math. (to appear)
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)
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)
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)
Bost, J.B.: To appear
Demailly, J.P.: Champs magnétiques et inégalités de Morse pour lad″ cohomologie. Ann. Inst. Fourier35, 189–229 (1985)
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 1986
Faltings, G.: Calculus on arithmetic surfaces. Ann. Math.119, 387–424 (1984)
Getzler, E.: An analogue of Demailly's inequality for strictly pseudoconvex manifolds. J. Diff. Geom.29, 231–244 (1989)
Gillet, H., Soulé, C.: Amplitude arithmétique. C.-R. Acad. Sc. Paris307, 887–890 (1988)
Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978
Greiner, P.: An asymptotic expansion for the heat equation. Arch. Ration. Mech. Anal.41, 163–218 (1971)
Quillen, D.: Determinants of Cauchy-Riemann operators. Funct. Anal. Appl.44, 31–34 (1985)
Ray, D.B., Singer, I.M.: Analytic torsion for complex manifolds. Ann. Math.98, 154–177 (1973)
Seeley, R.T.: Complex powers of an elliptic operator. Proc. Symp. Pure Math., Vol.10, pp. 288–307. Providence, R.I: Am. Math. Soc. 1967
Vojta, P.: An extension of the Thue-Siegel-Dyson-Gel'fond theorem. Preprint 1989
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
This paper was written while the first author was visiting the Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette) during the academic year 1987–1988
Rights and permissions
About this article
Cite this article
Bismut, JM., Vasserot, E. The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle. Commun.Math. Phys. 125, 355–367 (1989). https://doi.org/10.1007/BF01217912
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01217912