Determinant fiber bundles, Quillen metric and degeneracy of curves.

DOI10.1007/BF02391902zbMath0709.32019WikidataQ102245508 ScholiaQ102245508MaRDI QIDQ921201

Jean-Benoît Bost, Jean-Michel Bismut

Publication date: 1990

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

ordinary singularitiesfamily of complex curvesmetric of Quillentheory of Riemann-Roch-Grothendieck

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Divisors, linear systems, invertible sheaves (14C20) Holomorphic bundles and generalizations (32L05) Complex spaces (32C15)

Related Items

Semi-stability and heights of cycles ⋮ Adiabatic limits of \(\eta \)-invariants and the Meyer functions ⋮ Curvature of determinant bundles for degenerate families ⋮ On the singularity of Quillen metrics ⋮ Intrinsic heights of stable varieties and abelian varieties ⋮ Holomorphic extensions of Laplacians and their determinants ⋮ From the signature theorem to anomaly cancellation ⋮ Analytic torsion for surfaces with cusps. I: Compact perturbation theorem and anomaly formula ⋮ Remarks on the geometry of moduli spaces ⋮ Generalized holomorphic analytic torsion ⋮ Analytic torsion for surfaces with cusps. II: Regularity, asymptotics and curvature theorem ⋮ Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds ⋮ Surfaces with boundary: their uniformizations, determinants of Laplacians, and isospectrality ⋮ Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow ⋮ Quantum Hall effect and Quillen metric ⋮ Local index theorem for orbifold Riemann surfaces ⋮ Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants ⋮ Second variation of Selberg zeta functions and curvature asymptotics

Cites Work

• Unnamed Item
• Bilder und Urbilder analytischer Garben
• Algebraic geometry and the geometry of quantum strings
• Global gravitational anomalies
• Finiteness theorems for abelian varieties over number fields.
• Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces
• The logarithm of the Dedekind \(\eta\)-function
• Demailly's asymptotic Morse inequalities: a heat equation proof
• 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
• The analysis of elliptic families. I: Metrics and connections on determinant bundles
• Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). 2nd ed
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Stability of projective varieties
• Développement asymptotique des fonctions obtenues par intégration sur les fibres
• Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic section
• Über Modifikationen und exzeptionelle analytische Mengen
• The irreducibility of the space of curves of a given genus
• Curvature and the eigenvalues of the Laplacian
• Ein einfacher Beweis des Kohärenzsatzes von Grauert. (A simple proof of Grauert's coherence theorem)
• The singularities of the modulus space
• Spectral asymmetry and Riemannian Geometry. I
• Spectral asymmetry and Riemannian geometry. III
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Complex powers and asymptotic expansions. I. Functions of certain types.
• LOCALLY SEMIUNIVERSAL FLAT DEFORMATIONS OF ISOLATED SINGULARITIES OF COMPLEX SPACES