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

## TL;DR

This paper advances the understanding of the rational Picard group of Hitchin's spectral covers by expanding key divisors and deriving relations between Hodge classes, building on prior foundational work.

## Contribution

It generalizes previous results by expanding boundary, Maxwell stratum, and caustic divisors and establishes a new formula relating two Hodge classes in the moduli space.

## Key findings

- Expanded boundary, Maxwell stratum, and caustic divisors in the Picard group.
- Derived a formula relating two Hodge classes.
- Extended previous results on the discriminant divisor.

## Abstract

We continue the study of the rational Picard group of the moduli space of Hitchin's spectral covers started in P. Zograf's and D. Korotkin's work [11]. In the first part of the paper we expand the ``boundary'', ``Maxwell stratum'' and ``caustic'' divisors introduced in [11] via the set of standard generators of the rational Picard group. This generalizes the result of [11], where the expansion of the full discriminant divisor (which is a linear combination of the classes mentioned above) was obtained. In the second part of the paper we derive a formula that relates two Hodge classes in the rational Picard group of the moduli space of Hitchin's spectral covers.