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

TL;DR

This paper introduces universal Hitchin discriminants for Sp(2n) spectral covers, detailing their components and divisor classes within the moduli space, advancing understanding of spectral cover geometry.

Contribution

It defines and describes the universal Hitchin discriminants for Sp(2n) spectral covers, including their components and divisor classes in the moduli space.

Findings

Explicit description of Hitchin discriminants for Sp(2n) spectral covers

Expression of divisor classes in the rational Picard group

Analysis of components of the discriminants

Abstract

We define the universal Hitchin discriminants in the case of $\mathrm{Sp}(2n)$ Hitchin spectral covers, describe their components, and express their divisor classes in terms of standard generators of the rational Picard group of the moduli spaces of such spectral covers with variable base curve.