Second variation of Zhang's lambda-invariant on the moduli space of curves
Algebraic Geometry
2013-02-21 v2
Abstract
We compute the second variation of the \lambda-invariant, recently introduced by S. Zhang, on the complex moduli space M_g of curves of genus g>1, using work of N. Kawazumi. As a result we prove that (8g+4)\lambda is equal, up to a constant, to the \beta-invariant introduced some time ago by R. Hain and D. Reed. We deduce some consequences; for example we calculate the \lambda-invariant for each hyperelliptic curve, expressing it in terms of the Petersson norm of the discriminant modular form.
Keywords
Cite
@article{arxiv.1002.1618,
title = {Second variation of Zhang's lambda-invariant on the moduli space of curves},
author = {Robin de Jong},
journal= {arXiv preprint arXiv:1002.1618},
year = {2013}
}
Comments
13 pages