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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2312.05711 |
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| _version_ | 1866913609758539776 |
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| author | Klingner, Tyson |
| author_facet | Klingner, Tyson |
| contents | We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the $\mathrm{SO}_{2n+1}$-Hitchin fibration where the Higgs fields are $L$-twisted endomorphisms. Although the spectral data is known in the literature, we develop a new approach to spectral data, which takes advantage of Hecke modification. Further, we present the computation for the $\mathrm{Sp}_{2n}$ and $\mathrm{SO}_{2n}$ cases while clarifying some aspects of the correspondence which are not well explained in the pre-existing literature. We also compute the number of connected components of the generic fibres, and demonstrate Langlands duality in the fibres via the canonical duality in the fibres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05711 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral Data of Special Orthogonal Higgs Bundles and Hecke Modification Klingner, Tyson Algebraic Geometry We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the $\mathrm{SO}_{2n+1}$-Hitchin fibration where the Higgs fields are $L$-twisted endomorphisms. Although the spectral data is known in the literature, we develop a new approach to spectral data, which takes advantage of Hecke modification. Further, we present the computation for the $\mathrm{Sp}_{2n}$ and $\mathrm{SO}_{2n}$ cases while clarifying some aspects of the correspondence which are not well explained in the pre-existing literature. We also compute the number of connected components of the generic fibres, and demonstrate Langlands duality in the fibres via the canonical duality in the fibres. |
| title | Spectral Data of Special Orthogonal Higgs Bundles and Hecke Modification |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.05711 |