The Hitchin Fibration for Symmetric Pairs
Algebraic Geometry
2025-09-09 v3
Abstract
We introduce and describe the "regular quotient" for the Hitchin fibration for symmetric spaces and explain some basic consequences for Higgs bundles. We include an invariant theoretic approach to spectral covers in this setting for the particular space . We also include a study of the regular centralizer group scheme for quasisplit pairs, including a Galois description of a closely related group scheme. We collect some basic consequences for Hitchin systems associated to such pairs.
Cite
@article{arxiv.2407.00961,
title = {The Hitchin Fibration for Symmetric Pairs},
author = {Thomas Hameister and Benedict Morrissey},
journal= {arXiv preprint arXiv:2407.00961},
year = {2025}
}
Comments
v3: Heavily re-written. Figures added to section 3.4. Errors corrected proofs in Section 4. Section 5 expanded. Typos/small errors corrected throughout