Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212781 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-sheeted branched covering of the Riemann surface. In particular, we give a condition for Higgs bundles in the Hitchin section on ℂ or ℂ* to have compatible harmonic metrics.
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| ISSN: | 1815-0659 |