New explicit formulas for Faltings' delta-invariant

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

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