The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle

Jean-Michel Bismut; E. Vasserot

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 4, page 835-848
  • ISSN: 0373-0956

Abstract

top
The purpose of this paper is to calculate the asymptotics of the Ray-Singer analytic torsion associated with the p -th symmetric power of a holomorphic Hermitian positive vector bundle when p tends to + ∞ . We thus extend our previous results on positive line bundles.

How to cite

top

Bismut, Jean-Michel, and Vasserot, E.. "The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle." Annales de l'institut Fourier 40.4 (1990): 835-848. <http://eudml.org/doc/74901>.

@article{Bismut1990,
abstract = {The purpose of this paper is to calculate the asymptotics of the Ray-Singer analytic torsion associated with the $p$-th symmetric power of a holomorphic Hermitian positive vector bundle when $p$ tends to $+\infty $. We thus extend our previous results on positive line bundles.},
author = {Bismut, Jean-Michel, Vasserot, E.},
journal = {Annales de l'institut Fourier},
keywords = {asymptotics; Ray-Singer analytic torsion; holomorphic Hermitian positive vector bundle},
language = {eng},
number = {4},
pages = {835-848},
publisher = {Association des Annales de l'Institut Fourier},
title = {The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle},
url = {http://eudml.org/doc/74901},
volume = {40},
year = {1990},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 4
SP - 835
EP - 848
AB - The purpose of this paper is to calculate the asymptotics of the Ray-Singer analytic torsion associated with the $p$-th symmetric power of a holomorphic Hermitian positive vector bundle when $p$ tends to $+\infty $. We thus extend our previous results on positive line bundles.
LA - eng
KW - asymptotics; Ray-Singer analytic torsion; holomorphic Hermitian positive vector bundle
UR - http://eudml.org/doc/74901
ER -

References

top
  1. [B1] J. M. BISMUT, The index Theorem for families of Dirac operators: two heat equation proofs, Invent. Math., 83 (1987), 91-151. Zbl0592.58047MR87g:58117
  2. [B2] J. M. BISMUT, Demailly's asymptotic Morse inequalities: a heat equation proof, J. Funct. Anal., 72 (1987), 263-278. Zbl0649.58030MR88j:58131
  3. [BGS1] J. M. BISMUT, H. GILLET, C. SOULÉ, Analytic torsion and holomorphic determinant bundles. II, Comm. Math. Phys., 115 (1988), 79-126. Zbl0651.32017MR89g:58192b
  4. [BGS2] J. M. BISMUT, H. GILLET, C. SOULÉ, Analytic torsion and holomorphic determinant bundles. III, Comm. Math. Phys., 115 (1988), 301-351. Zbl0651.32017MR89g:58192c
  5. [BV] J. M. BISMUT, E. VASSEROT. The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Comm. Math. Phys., 125 (1989), 355-367. Zbl0687.32023MR91c:58141
  6. [De] J. P. DEMAILLY, 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. Zbl0651.32019MR89k:32058
  7. [Ge] E. GETZLER, Inégalités asymptotiques de Demailly pour les fibrés vectoriels, C.R. Acad. Sci., Série I. Math., 304 (1987), 475-478. Zbl0614.32022MR88j:32040
  8. [GrH] P. GRIFFITHS, J. HARRIS, Principles of algebraic geometry, New York, Wiley, 1978. Zbl0408.14001MR80b:14001
  9. [K] S. KOBAYASHI, Differential geometry of complex vector bundles, Iwanami Shoten and Princeton University Press, 1987. Zbl0708.53002MR89e:53100
  10. [LP] J. LE POTIER, Théorèmes d'annulation en cohomologie, C.R. Acad. Sci. Paris, Série A, 276 (1976), 535-537. Zbl0249.32021MR49 #7482
  11. [Q] D. QUILLEN, Superconnections and the Chern character, Topology, 24 (1985), 89-95. Zbl0569.58030MR86m:58010
  12. [RS] D. B. RAY, I. M. SINGER, Analytic torsion for complex manifolds, Ann. of Math., 98 (1973), 154-177. Zbl0267.32014MR52 #4344
  13. [Se] R. T. SEELEY, Complex powers of an elliptic operator, Proc. Symp. Pure and Appl. Math., Vol. 10, 288-307, Providence, Am. Math. Soc., (1967). Zbl0159.15504MR38 #6220

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.