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arXiv · 2108.12911

Variational formulas on spaces of SL(2) Hitchin's spectral covers

R. Klimov
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Abstract

Using the developed deformation theory on moduli spaces of quadratic differentials we derive variational formulas for objects associated with generalized $SL(2)$ Hitchin's spectral covers: Prym matrix, Prym bidifferential, Hodge and Prym tau-functions. The resulting formulas are antisymmetric versions of Donagi-Markman residue formula. The second variation of the Prym matrix is a natural analogy to the expression previously derived for the period matrix of the $GL(n)$ spectral cover.

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R. Klimov. 2021-08-29. Variational formulas on spaces of SL(2) Hitchin's spectral covers. https://arxiv.org/abs/2108.12911

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