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Spectral Data for Spin Higgs Bundles
Abstract In this paper we determine the spectral data parametrizing Higgs bundles in a generic fiber of the Hitchin map for the case where the structure group is the special Clifford group with fixed Clifford norm. These are spin and “twisted” spin Higgs bundles. The method used relates variations in spectral data with respect to the Hecke transformations for orthogonal bundles introduced by Abe. The explicit description also recovers a result from the geometric Langlands program, which states that the fibers of the Hitchin map are the dual abelian varieties to the corresponding fibers of the moduli spaces of projective orthogonal Higgs bundles (in the even case) and projective symplectic Higgs bundles (in the odd case).
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- Award ID(s):
- 1906403
- PAR ID:
- 10285995
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2021
- Issue:
- 6
- ISSN:
- 1073-7928
- Page Range / eLocation ID:
- 4211 to 4230
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imrn/rny296
