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

References in corpus (4)

• Langlands duality and G2 spectral curves
• Moduli of Parabolic Higgs Bundles and Atiyah Algebroids
• Global nilpotent cone is isotropic : parahoric torsors on curves
• Jordan blocks of Richardson classes in the classical groups and the Bala--Carter Theorem

Cited by in corpus (7)

• Singular Geometry and Higgs Bundles in String Theory
• Moduli spaces of generalized hyperpolygons
• Tamely ramified geometric Langlands correspondence in positive characteristic
• Parabolic Hitchin Maps and Their Generic Fibers
• Mirror symmetry for parabolic Higgs bundles via $p$-adic integration
• Equality of the wobbly and shaky loci
• The Hitchin Image in Type-D