The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle
type: Item
instance of: scholarly article
title: The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle
zbMATH Open document ID: 0687.32023
DOI: 10.1007/BF01217912
author: Jean-Michel Bismut
author: Eric Vasserot
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: Let M be a compact complex manifold equipped with a smooth hermitian metric, \(\zeta\) a holomorphic hermitian vector bundle, \(\mu\) a positive hermitian line bundle. Let \(e_ p\), \(p\in {\mathbb{N}}\), be a holomorphic hermitian flat vector bundle. Assume \(\mu\) is equipped with a metric whose curvature is positive and let \(\tau_ p\) be the Ray-Singer analytic torsion of the Dolbeault complex on \(\mu^{\otimes p}\otimes \zeta \otimes E_ p\) [\textit{D. B. Ray} and \textit{I. M. Singer}, Ann. Math., II. Ser. 98, 154-177 (1973; Zbl 0267.32014). In the paper the authors establish an asymptotic formula for Log \(\tau_ p\) as \(p\to +\infty\).
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 58A10
zbMATH DE Number: 4125795
zbMATH Keywords: hermitian metric
zbMATH Keywords: holomorphic hermitian vector bundle
zbMATH Keywords: Ray-Singer analytic torsion
reviewed by: Giuseppe Tomassini
MaRDI profile type: Publication
cites work: Demailly's asymptotic Morse inequalities: a heat equation proof
cites work: Superconnection currents and complex immersions
cites work: Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
cites work: Q3807546
cites work: Champs magnétiques et inégalités de Morse pour la d''-cohomologie. (Magnetic fields and Morse inequalities for d''-cohomology)
cites work: Calculus on arithmetic surfaces
cites work: An analogue of Demailly's inequality for strictly pseudoconvex CR manifolds
cites work: Q3831122
cites work: Q4195061
cites work: An asymptotic expansion for the heat equation
cites work: Determinants of Cauchy-Riemann operators on a Riemann surface
cites work: Analytic torsion for complex manifolds
cites work: Q5542418
full work available at URL: https://doi.org/10.1007/bf01217912
OpenAlex ID: W2011124352
description: scientific article; zbMATH DE number 4125795