Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916517429379072 |
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| author | Fujioka, Hitoshi |
| author_facet | Fujioka, Hitoshi |
| contents | 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 $\mathbb{C}$ or $\mathbb{C}^*$ to have compatible harmonic metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section Fujioka, Hitoshi Differential Geometry 53C07, 14D21 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 $\mathbb{C}$ or $\mathbb{C}^*$ to have compatible harmonic metrics. |
| title | Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section |
| topic | Differential Geometry 53C07, 14D21 |
| url | https://arxiv.org/abs/2403.07258 |