In this paper we compute the asymptotics of the natural metric on the line bundle over the moduli space ℳ g associated to the algebraic cycle C–C – in the jacobian Jac C of a smooth projective curve C of genus g ≥ 3. The asymptotics are related to the structure of the mapping class group of a genus g surface.
"On the Arakelov Geometry of Moduli Spaces of Curves." J. Differential Geom. 67 (2) 195 - 228, June 2004. https://doi.org/10.4310/jdg/1102536200