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

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.
Comment: 10 pages, 6 figures