Comparison of the Hitchin metric and the semi-flat metric in the rank two case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914860612190208 |
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| author | Mochizuki, Takuro |
| author_facet | Mochizuki, Takuro |
| contents | Let $(E,θ)$ be a Higgs bundle of rank $2$ and degree $0$ on a compact Riemann surface $X$ whose spectral curve is smooth. The tangent space of the moduli space of Higgs bundles at $(E,θ)$ is equipped with two natural metrics called the Hitchin metric and the semi-flat metric. It is known that the difference between two metrics along the curve $(E,tθ)$ $(t\geq 1)$ decays in an exponential way. In this paper, we shall study how the exponential rate is improved. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_05188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparison of the Hitchin metric and the semi-flat metric in the rank two case Mochizuki, Takuro Differential Geometry Algebraic Geometry 53C07, 58E15, 14D21, 81T13 Let $(E,θ)$ be a Higgs bundle of rank $2$ and degree $0$ on a compact Riemann surface $X$ whose spectral curve is smooth. The tangent space of the moduli space of Higgs bundles at $(E,θ)$ is equipped with two natural metrics called the Hitchin metric and the semi-flat metric. It is known that the difference between two metrics along the curve $(E,tθ)$ $(t\geq 1)$ decays in an exponential way. In this paper, we shall study how the exponential rate is improved. |
| title | Comparison of the Hitchin metric and the semi-flat metric in the rank two case |
| topic | Differential Geometry Algebraic Geometry 53C07, 58E15, 14D21, 81T13 |
| url | https://arxiv.org/abs/2407.05188 |