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

TL;DR

This paper derives variational formulas for objects related to $SL(2)$ Hitchin spectral covers, extending deformation theory and providing antisymmetric residue formulas and second variation analogies.

Contribution

It introduces new variational formulas for Prym-related objects on $SL(2)$ spectral covers, expanding deformation theory applications.

Findings

Derived antisymmetric residue formulas for spectral cover objects

Established second variation formulas for Prym matrix

Connected Prym and period matrix variations in spectral cover theory

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.