Spectral data for parabolic projective symplectic/orthogonal Higgs bundles

TL;DR

This paper describes the structure of generic Hitchin fibers for moduli spaces of stable parabolic projective symplectic and orthogonal Higgs bundles, extending Hitchin's foundational work to new cases.

Contribution

It provides a detailed description of the generic Hitchin fibers for these moduli spaces, including cases with and without fixed determinants.

Findings

Describes generic Hitchin fibers for parabolic projective symplectic Higgs bundles.

Describes generic Hitchin fibers for orthogonal Higgs bundles.

Includes cases with trivial and non-trivial determinants.

Abstract

Hitchin in [Duke Math. J. 54 (1), 91-114 (1987)] introduced a proper morphism from the moduli space of stable $G$-Higgs bundles ($G=\mathrm{GL}(n,\mathbb{C}),\mathrm{Sp}(2m,\mathbb{C})$ and $\mathrm{SO}(n,\mathbb{C})$) over a curve to a vector space of invariant polynomials and he described the generic fibers of that morphism. In this paper, we first describe the generic Hitchin fibers for the moduli space of stable parabolic projective symplectic/orthogonal Higgs bundles without fixing the determinant. We also describe the generic fibers when the determinant is trivial.