New explicit formulas for Faltings' delta-invariant
Algebraic Geometry
2016-12-06 v3 Number Theory
Abstract
In this paper we give new explicit formulas for Faltings' -invariant in terms of integrals of theta functions, and we deduce an explicit lower bound for only in terms of the genus and an explicit upper bound for the Arakelov-Green function in terms of . Furthermore, we give a canonical extension of and the Zhang-Kawazumi invariant to the moduli space of indecomposable principally polarised complex abelian varieties.
Cite
@article{arxiv.1605.00847,
title = {New explicit formulas for Faltings' delta-invariant},
author = {Robert Wilms},
journal= {arXiv preprint arXiv:1605.00847},
year = {2016}
}
Comments
46 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