Asymptotic behavior of Faltings's delta function

DOI10.1215/S0012-7094-90-06111-3zbMath0746.30032OpenAlexW1991958464MaRDI QIDQ1813347

Jay A. Jorgenson

Publication date: 25 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-90-06111-3

zbMATH Keywords

Green's functionArakelov-Faltings' theoryFaltings \(\delta\)-functionRiemann \(\theta\)-function

Mathematics Subject Classification ID

Harmonic functions on Riemann surfaces (30F15) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (15)

Arakelov geometry on degenerating curves ⋮ Bounds on Faltings's delta function through covers ⋮ The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces ⋮ New explicit formulas for Faltings' delta-invariant ⋮ Applications of Kronecker's limit formula for elliptic Eisenstein series ⋮ Effective bounds for Faltings's delta function ⋮ Non-completeness of the Arakelov-induced metric on moduli space of curves ⋮ Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface ⋮ Convergence of eigenvalues and Green functions under surgery type degeneration of Riemannian manifolds ⋮ Precise constants in bosonization formulas on Riemann surfaces. I ⋮ Analytic torsion for line bundles on Riemann surfaces ⋮ The asymptotics of the Arakelov-Green's function and Faltings' delta invariant ⋮ On the asymptotics of determinant of Laplacian at the principal boundary of the principal stratum of the moduli space of Abelian differentials ⋮ Boundary asymptotics of the relative Bergman kernel metric for curves ⋮ The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces

Cites Work

• Calculus on arithmetic surfaces
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Theta functions on Riemann surfaces
• Theta functions, kernel functions, and Abelian integrals
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
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