Submersions and equivariant Quillen metrics

DOI10.5802/aif.1800zbMath0964.58025OpenAlexW2318661794MaRDI QIDQ1586375

Xiaonan Ma

Publication date: 13 November 2000

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2000__50_5_1539_0

zbMATH Keywords

cohomologyQuillen metriccomplex manifoldsubmersiondeterminant line bundleequivariant analytic torsion forms

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Determinants and determinant bundles, analytic torsion (58J52) Holomorphic bundles and generalizations (32L05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25)

Related Items (18)

The direct image of a flat fibration with complex fibers ⋮ The Weil-Petersson current for moduli of vector bundles and applications to orbifolds ⋮ Comparison of two equivariant \(\eta\)-forms ⋮ Analytic torsion for log-Enriques surfaces and Borcherds product ⋮ Analytic torsion forms for fibrations by projective curves ⋮ The asymptotics of the holomorphic analytic torsion forms ⋮ \(K3\) surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space. III: The case \(r(M) \geq 18\) ⋮ K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: The structure of the invariant ⋮ $K3$ surfaces with involution and analytic torsion ⋮ Equivariant eta forms and equivariant differential \(K\)-theory ⋮ Orbifolds and analytic torsions ⋮ Analytic torsion of Hirzebruch surfaces ⋮ A fixed point formula of Lefschetz type in Arakelov geometry. I: Statement and proof ⋮ Torsion type invariants of singularities ⋮ A Trinity of the Borcherds Φ-Function ⋮ The holomorphic torsion forms of the de Rham complex ⋮ Orbifold Submersion and Analytic Torsions ⋮ Families of equivariant immersions and analytic torsion forms

Cites Work

• The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas
• Superconnection currents and complex immersions
• Superconnections and the Chern character
• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• Determinants of Cauchy-Riemann operators on a Riemann surface
• A short proof of the local Atiyah-Singer index theorem
• 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
• Analytic torsion and the arithmetic Todd genus. (With an appendix by D. Zagier)
• Complex immersions and Quillen metrics
• Equivariant immersions and Quillen metrics
• An arithmetic Riemann-Roch theorem
• A Lefschetz fixed point formula for elliptic complexes. I
• Curvature and the eigenvalues of the Laplacian
• On the heat equation and the index theorem
• Analytic torsion for complex manifolds
• Adiabatic Limit, Heat Kernel and Analytic Torsion
• Koszul Complexes, Harmonic Oscillators, and the Todd Class
• η-Invariants and Their Adiabatic Limits
• Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Un théorème du point fixe de Lefschetz en géométrie d'Arakelov
• Quillen metrics and higher analytic torsion forms.
• Formes de torsion analytique et familles de submersions
• Formes de torsion analytique et familles des submersions I
• A fixed point formula of Lefschetz type in Arakelov geometry. I: Statement and proof
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