New explicit formulas for Faltings' delta-invariant

• 成果类型: Article
• 署名作者: Wilms, Robert
• 署名单位: Johannes Gutenberg University of Mainz
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0713-1
• 发表日期: 2017
• 页码: 481-539
• 关键词: riemann surfaces; arakelov invariants; asymptotic-behavior; theta-functions; kawazumi-zhang; CURVES; bounds; genus-2

摘要

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.