# On the image of the parabolic Hitchin map

## TL;DR

This paper characterizes the image of the parabolic Hitchin map across classical groups and G2, revealing it is generally affine space, with exceptions for certain 'bad' parabolics in type D where singularities occur.

## Contribution

It provides a comprehensive determination of the Hitchin map's image for all parabolics in classical groups and G2, highlighting cases with singularities.

## Key findings

- Image is affine space for all parabolics except specific type D cases.
- Identifies 'bad parabolics' where the image can be singular.
- Provides explicit descriptions of the Hitchin map's image.

## Abstract

We determine the image of the (strongly) parabolic Hitchin map for all parabolics in classical groups and $G_2$. Surprisingly, we find that the image is isomorphic to an affine space in all cases, except for certain "bad parabolics" in type $D$, where the image can be singular.