Spaces of Abelian Differentials and Hitchin's Spectral Covers

Using the embedding of the moduli space of generalized GL(n) Hitchin's spectral covers to the moduli space of meromorphic Abelian differentials we study the variational formulae of the period matrix, the canonical bidifferential, the prime form and the Bergman tau function. This leads to residue formulae which generalize the Donagi-Markman formula for variations of the period matrix. The computation of second derivatives of the period matrix reproduces the formula derived in [2] using the framework of topological recursion.

Automated summary

By using the embedding of the moduli space of generalized GL(n) Hitchin's spectral covers into the moduli space of meromorphic Abelian differentials, variational formulae for the period matrix, canonical bidifferential, prime form, and Bergman tau function were studied, leading to generalize the residue formulae from Donagi-Markman's formula. The computation of second derivatives of the period matrix reproduces the formula derived in [2] using the framework of topological recursion.