Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910002596282368 |
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| author | Mochizuki, Takuro |
| author_facet | Mochizuki, Takuro |
| contents | The moduli space of stable Higgs bundles of degree $0$ is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperkähler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray $(E,tθ)$ as $t\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_17638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles Mochizuki, Takuro Differential Geometry Algebraic Geometry 53C07, 58E15, 14D21, 81T13 The moduli space of stable Higgs bundles of degree $0$ is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperkähler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray $(E,tθ)$ as $t\to\infty$. |
| title | Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles |
| topic | Differential Geometry Algebraic Geometry 53C07, 58E15, 14D21, 81T13 |
| url | https://arxiv.org/abs/2305.17638 |