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

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.

V2: 22 pages, some minor corrections

References in corpus (1)

• Class of discriminant for $\mathrm{Sp}(2n)$ Hitchin spectral covers

Cited by in corpus (1)

• On Generalized WKB Expansion of Monodromy Generating Function