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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212781 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862621348152475648 |
|---|---|
| author | Fujioka, Hitoshi |
| author_facet | Fujioka, Hitoshi |
| citation_txt | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T11:56:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212781 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:56:06Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fujioka, Hitoshi 2026-02-11T10:37:43Z 2024 Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages 1815-0659 2020 Mathematics Subject Classification: 53C07; 14D21 arXiv:2403.07258 https://nasplib.isofts.kiev.ua/handle/123456789/212781 https://doi.org/10.3842/SIGMA.2024.111 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. The author is grateful to the referees for their careful reading and valuable comments. The author is grateful to his supervisor, Takuro Mochizuki, for many discussions and helpful advice. The author thanks Qiongling Li and Takashi Ono for their helpful advice. This work was supported by JST SPRING, Grant Number JPMJSP2110. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section Article published earlier |
| spellingShingle | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section Fujioka, Hitoshi |
| title | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section |
| title_full | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section |
| title_fullStr | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section |
| title_full_unstemmed | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section |
| title_short | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section |
| title_sort | harmonic metrics for higgs bundles of rank 3 in the hitchin section |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212781 |
| work_keys_str_mv | AT fujiokahitoshi harmonicmetricsforhiggsbundlesofrank3inthehitchinsection |