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

Abstract

We compute the second variation of the λ-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)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.

13 pages

References in corpus (2)

• Johnson's homomorphisms and the Arakelov-Green function
• Geometric Proofs of Some Results of Morita

Cited by in corpus (3)

• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Normal functions and the height of Gross-Schoen cycles
• Symmetric roots and admissible pairing