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arXiv · 1812.05789

Spaces of abelian differentials and Hitchin's spectral covers

Marco Bertola·Dmitry Korotkin
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Abstract

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. Computation of second derivatives of the period matrix reproduces the formula derived by Baraglia and Zhenxi Huang using the framework of topological recursion.

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Marco Bertola, Dmitry Korotkin. 2018-12-14. Spaces of abelian differentials and Hitchin's spectral covers. https://arxiv.org/abs/1812.05789

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