Tau functions, Hodge classes and discriminant loci on moduli spaces of Hitchin's spectral covers

Abstract

We define two tau functions, $\tau$ and $\hat{\tau }$ , on moduli spaces of spectral covers of $GL(n)$ Hitchin's systems. Analyzing the properties of $\tau$, we express the divisor class of the universal Hitchin's discriminant in terms of standard generators of the rational Picard group of the moduli spaces of spectral covers with variable base. The function $\hat{\tau }$ is used to compute the divisor of canonical 1-forms with multiple zeros.

Dedicated to the memory of L.D.Faddeev, ed. by A.Its and N.Reshetikhin

References in corpus (1)

• Donagi-Markman cubic for the generalised Hitchin system

Cited by in corpus (1)

• Discriminant and Hodge classes on the space of Hitchin's covers