Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915115685642240 |
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| author | Mochizuki, Takuro |
| author_facet | Mochizuki, Takuro |
| contents | We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero degree case, we introduce the semi-flat metric, and compare the asymptotic behaviour of the semi-flat metric and the Hitchin metric along the ray $(E,tθ)$ $(t\to\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case Mochizuki, Takuro Algebraic Geometry 53C07, 58E15, 14D21, 81T13 We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero degree case, we introduce the semi-flat metric, and compare the asymptotic behaviour of the semi-flat metric and the Hitchin metric along the ray $(E,tθ)$ $(t\to\infty)$. |
| title | Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case |
| topic | Algebraic Geometry 53C07, 58E15, 14D21, 81T13 |
| url | https://arxiv.org/abs/2501.12741 |