On the image of the parabolic Hitchin map

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.

In this paper we compute the base of the strongly parabolic Hitchin map. In the companion paper arXiv:1608.05454 we prove that this gives a completely integrable system