The purpose of this paper is to calculate the asymptotics of the Ray-Singer analytic torsion associated with the -th symmetric power of a holomorphic Hermitian positive vector bundle when tends to . We thus extend our previous results on positive line bundles.
L’objet de cet article est de calculer le comportement asymptotique de la torsion analytique de Ray-Singer associée à la -ième puissance symétrique d’un fibré vectoriel holomorphe Hermitien positif quand tend vers . Nous étendons ainsi notre résultat antérieur relatif aux fibrés en droites positifs.
@article{AIF_1990__40_4_835_0, author = {Bismut, Jean-Michel and Vasserot, E.}, title = {The asymptotics of the {Ray-Singer} analytic torsion of the symmetric powers of a positive vector bundle}, journal = {Annales de l'Institut Fourier}, pages = {835--848}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {40}, number = {4}, year = {1990}, doi = {10.5802/aif.1237}, zbl = {0711.32015}, mrnumber = {92b:58237}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1237/} }
TY - JOUR AU - Bismut, Jean-Michel AU - Vasserot, E. TI - The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle JO - Annales de l'Institut Fourier PY - 1990 SP - 835 EP - 848 VL - 40 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1237/ DO - 10.5802/aif.1237 LA - en ID - AIF_1990__40_4_835_0 ER -
%0 Journal Article %A Bismut, Jean-Michel %A Vasserot, E. %T The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle %J Annales de l'Institut Fourier %D 1990 %P 835-848 %V 40 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1237/ %R 10.5802/aif.1237 %G en %F AIF_1990__40_4_835_0
Bismut, Jean-Michel; Vasserot, E. The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 835-848. doi : 10.5802/aif.1237. https://aif.centre-mersenne.org/articles/10.5802/aif.1237/
[B1] The index Theorem for families of Dirac operators: two heat equation proofs, Invent. Math., 83 (1987), 91-151. | EuDML | MR | Zbl
,[B2] Demailly's asymptotic Morse inequalities: a heat equation proof, J. Funct. Anal., 72 (1987), 263-278. | MR | Zbl
,[BGS1] Analytic torsion and holomorphic determinant bundles. II, Comm. Math. Phys., 115 (1988), 79-126. | MR | Zbl
, , ,[BGS2] Analytic torsion and holomorphic determinant bundles. III, Comm. Math. Phys., 115 (1988), 301-351. | MR | Zbl
, , ,[BV] The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Comm. Math. Phys., 125 (1989), 355-367. | MR | Zbl
, .[De] Vanishing theorems for tensor powers of a positive vector bundle. In Geometry and Analysis, T. Sunada, ed., pp. 86-106, Lecture Notes in Math. Berlin-Heidelberg-New York, Springer-Verlag, 1988. | MR | Zbl
,[Ge] Inégalités asymptotiques de Demailly pour les fibrés vectoriels, C.R. Acad. Sci., Série I. Math., 304 (1987), 475-478. | MR | Zbl
,[GrH] Principles of algebraic geometry, New York, Wiley, 1978. | MR | Zbl
, ,[K] Differential geometry of complex vector bundles, Iwanami Shoten and Princeton University Press, 1987. | MR | Zbl
,[LP] Théorèmes d'annulation en cohomologie, C.R. Acad. Sci. Paris, Série A, 276 (1976), 535-537. | MR | Zbl
,[Q] Superconnections and the Chern character, Topology, 24 (1985), 89-95. | MR | Zbl
,[RS] Analytic torsion for complex manifolds, Ann. of Math., 98 (1973), 154-177. | MR | Zbl
, ,[Se] Complex powers of an elliptic operator, Proc. Symp. Pure and Appl. Math., Vol. 10, 288-307, Providence, Am. Math. Soc., (1967). | MR | Zbl
,Cited by Sources: