Bounds on Faltings’s Delta Function Through Covers
نویسندگان
چکیده
Let X be a compact Riemann surface of genus g X ≥ 1. In [7], G. Falt-ings introduced a new invariant δ Fal (X) associated to X. In this paper we give explicit bounds for δ 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).
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تاریخ انتشار 2006