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arXiv · 1605.00847

New explicit formulas for Faltings' delta-invariant

Robert Wilms
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Abstract

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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Robert Wilms. 2016-12-03. New explicit formulas for Faltings' delta-invariant. https://doi.org/10.1007/s00222-016-0713-1

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