On the arakelov geometry of moduli spaces of curves

Abstract

In this paper we compute the asymptotics of the natural metric on the line bundle over the moduli spaceMg 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. © 2004 Applied Probability Trust.