On the image of the parabolic Hitchin map

David Baraglia; Masoud Kamgarpour

doi:10.1093/qmath/hax055

On the image of the parabolic Hitchin map

Algebraic Geometry 2018-06-11 v1 Representation Theory

Authors: David Baraglia , Masoud Kamgarpour

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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.

Keywords

parabolic Hitchin map classical groups affine space singular image parabolic structures

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@article{arxiv.1703.09886,
  title  = {On the image of the parabolic Hitchin map},
  author = {David Baraglia and Masoud Kamgarpour},
  journal= {arXiv preprint arXiv:1703.09886},
  year   = {2018}
}

Comments

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

On the image of the parabolic Hitchin map

Abstract

Keywords

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