2016/05/31 by Robert Wilms
Mathematics · #Abelian group #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Indecomposable module #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Moduli space #Pure mathematics #Upper and lower bounds #math.AG #math.NT #msc:11G30 #msc:14G40 #msc:14H42 #msc:14H55 #msc:14K25
paper · pdf · doi:10.1007/s00222-016-0713-1
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
openalex publication_date 2016/12/02 · arxiv created 2016/12/03 · arxiv updated 2016/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.