Faltings delta-invariant and semistable degeneration

Abstract

We determine the asymptotic behavior of the Arakelov metric, the Arakelov-Green's function, and the Faltings delta-invariant for arbitrary one-parameter families of complex curves with semistable degeneration. The leading terms in the asymptotics are given a combinatorial interpretation in terms of S. Zhang's theory of admissible Green's functions on polarized metrized graphs.

50 pages

References in corpus (3)

• Asymptotics of degenerations of mixed Hodge structures
• New explicit formulas for Faltings' delta-invariant
• SL_2-orbits and degenerations of mixed Hodge structure

Cited by in corpus (9)

• Canonical measures on metric graphs and a Kazhdan's theorem
• Positivity of the height jump divisor
• Limits of canonical forms on towers of Riemann surfaces
• Degeneration of Riemann theta functions and of the Zhang-Kawazumi invariant with applications to a uniform Bogomolov conjecture
• Jumps in the height of the Ceresa cycle
• Boundary asymptotics of the relative Bergman kernel metric for curves
• Effective upper bound of analytic torsion under Arakelov metric
• Chern-Weil theory for line bundles with the family Arakelov metric
• Asymptotic Behavior of the Zhang--Kawazumi's phi-invariant