Second variation of Zhang's lambda-invariant on the moduli space of curves

Details Second variation of Zhang's lambda-invariant on the moduli space of curves Second variation of Zhang's lambda-invariant on the moduli space of curves

2010-02-08

arxiv.org/abs/1002.1618v2

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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.

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