Submersions and equivariant Quillen metrics
type: Item
instance of: scholarly article
title: Submersions and equivariant Quillen metrics
zbMATH Open document ID: 0964.58025
author: Xiaonan Ma
publication date: 2000-11-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75464
review text: This paper fits in the program, developed by J.-M. Bismut, of calculating Quillen metrics of the line bundle sections arising canonically from geometrically defined isomorphisms of inverse determinant cohomology bundles on compact complex manifolds. Previous examples of such work include: \textit{J.-M. Bismut} and \textit{G. Lebeau} [Publ. Math., Inst. Hautes Etud. Sci. 74, 1-297 (1991; Zbl 0784.32010)] on immersions; \textit{A. Berthomieu} and \textit{J.-M. Bismut} [J. Reine Angew. Math. 457, 85-184 (1994; Zbl 0804.32017)] on submersions; and \textit{J.-M. Bismut} [J. Differ. Geom. 41, 53-157 (1995; Zbl 0826.32024)] on equivariant immersions. The paper under review handles the case of a submersion of compact complex manifolds, equivariant with respect to the holomorphic action of a compact Lie group. The formula for the Quillen metric involves equivariant analytic torsion forms.
reviewed by: Peter Haskell
Mathematics Subject Classification ID: 58J52
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 32J25
zbMATH DE Number: 1528715
zbMATH Keywords: Quillen metric
zbMATH Keywords: determinant line bundle
zbMATH Keywords: cohomology
zbMATH Keywords: equivariant analytic torsion forms
zbMATH Keywords: complex manifold
zbMATH Keywords: submersion
MaRDI profile type: Publication
OpenAlex ID: W2318661794
cites work: A Lefschetz fixed point formula for elliptic complexes. I
cites work: On the heat equation and the index theorem
cites work: Q4002484
cites work: Quillen metrics and higher analytic torsion forms.
cites work: The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
cites work: Superconnection currents and complex immersions
cites work: Koszul Complexes, Harmonic Oscillators, and the Todd Class
cites work: Q4312301
cites work: Equivariant immersions and Quillen metrics
cites work: Q4393472
cites work: The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas
cites work: η-Invariants and Their Adiabatic Limits
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: Q5288191
cites work: Complex immersions and Quillen metrics
cites work: Q3891073
cites work: Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
cites work: Adiabatic Limit, Heat Kernel and Analytic Torsion
cites work: A short proof of the local Atiyah-Singer index theorem
cites work: Q4195061
cites work: Analytic torsion and the arithmetic Todd genus. (With an appendix by D. Zagier)
cites work: An arithmetic Riemann-Roch theorem
cites work: The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
cites work: Q4819931
cites work: Un théorème du point fixe de Lefschetz en géométrie d'Arakelov
cites work: A fixed point formula of Lefschetz type in Arakelov geometry. I: Statement and proof
cites work: Formes de torsion analytique et familles de submersions
cites work: Formes de torsion analytique et familles des submersions I
cites work: Curvature and the eigenvalues of the Laplacian
cites work: Determinants of Cauchy-Riemann operators on a Riemann surface
cites work: Superconnections and the Chern character
cites work: Analytic torsion for complex manifolds
cites work: Q3900552
DOI: 10.5802/AIF.1800
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1528715