Abstract
Let X be a compact Riemann surface of genus gX 1. In 1984, G. Faltings introduced a new invariant Fal(X) associated to X. In this paper we give explicit bounds for Fal(X) in terms of fundamental dierential geometric invariants arising from X, when gX > 1. As an application, we are able to give bounds for Faltings’s delta function for the family of modular curves X0(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 J0(N) associated to X0(N).
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