Bounds on Faltings's delta function through covers

• 成果类型: Article
• 署名作者: Jorgenson, Jay; Kramer, Juerg
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.1
• 发表日期: 2009
• 页码: 1-43
• 关键词: raumformen und bewegungsgruppen; prime geodesic theorem; modular-curves x-0(n); arithmetic surfaces; riemann surfaces; determinants; laplacians; forms

摘要

Let X be a compact Riemann surface of genus g(X) >= 1. In 1984, G. Faltings introduced a new invariant delta(Fal) (X) associated to X. In this paper we give explicit bounds for delta(Fal)(X) in terms of fundamental differential geometric invariants arising from X, when g(X) > 1. As an application, we are able to give bounds for Faltings's delta function for the family of modular curves X-0(N) in terms of the genus only. In combination with work of A. Abbes, P. Michel and E. Ullmo, this leads to an asymptotic formula for the Faltings height of the Jacobian J(0)(N) associated to X-0(N).