Journal of Differential Geometry

Faltings delta-invariant and semistable degeneration

Robin de Jong

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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.

Article information

Source
J. Differential Geom., Volume 111, Number 2 (2019), 241-301.

Dates
Received: 3 November 2016
First available in Project Euclid: 6 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1549422102

Digital Object Identifier
doi:10.4310/jdg/1549422102

Mathematical Reviews number (MathSciNet)
MR3909908

Zentralblatt MATH identifier
07015570

Citation

de Jong, Robin. Faltings delta-invariant and semistable degeneration. J. Differential Geom. 111 (2019), no. 2, 241--301. doi:10.4310/jdg/1549422102. https://projecteuclid.org/euclid.jdg/1549422102


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