New explicit formulas for Faltings' delta-invariant

Abstract

In this paper we give new explicit formulas for Faltings' $\delta$-invariant in terms of integrals of theta functions, and we deduce an explicit lower bound for $\delta$ only in terms of the genus and an explicit upper bound for the Arakelov-Green function in terms of $\delta$. Furthermore, we give a canonical extension of $\delta$ and the Zhang-Kawazumi invariant $\phi$ to the moduli space of indecomposable principally polarised complex abelian varieties.

arXiv comment46 pages. The final publication will appear in Inventiones Mathematicae and is available at link.springer.com/article/10.1007/s00222-016-0713-1. This paper replaces the older paper arXiv:1505.04740, which only treats a special case

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• Geometric Proofs of Some Results of Morita
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Cited by in corpus (9)

• Faltings delta-invariant and semistable degeneration
• Néron-Tate heights of cycles on jacobians
• On arithmetic intersection numbers on self-products of curves
• Degeneration of Riemann theta functions and of the Zhang-Kawazumi invariant with applications to a uniform Bogomolov conjecture
• Heights, ranks and regulators of abelian varieties
• Jumps in the height of the Ceresa cycle
• Heights on square of modular curves
• Frobenius' theta function and Arakelov invariants in genus three
• The Genus Two Free Boson in Arakelov Geometry