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

الأصل · EN

We compute the second variation of the λ-invariant, recently introduced by S. Zhang, on the complex moduli space Mg of curves of genus g>1, using work of N. Kawazumi. As a result we prove that (8g+4)λis equal, up to a constant, to the β-invariant introduced some time ago by R. Hain and D. Reed. We deduce some consequences; for example we calculate the λ-invariant for each hyperelliptic curve, expressing it in terms of the Petersson norm of the discriminant modular form.