Isolated singularities of Toda equations and cyclic Higgs bundles
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911763265486848 |
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| author | Li, Qiongling Mochizuki, Takuro |
| author_facet | Li, Qiongling Mochizuki, Takuro |
| contents | This paper is the second part of our study on the Toda equations and the cyclic Higgs bundles associated to $r$-differentials over non-compact Riemann surfaces. We classify all the solutions up to boundedness around the isolated singularity of an $r$-differential under the assumption that the $r$-differential is meromorphic or has some type of essential singularity. As a result, for example, we classify all the solutions on ${\mathbb C}$ if the $r$-differential is a finite sum of the exponential of polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_06129 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Isolated singularities of Toda equations and cyclic Higgs bundles Li, Qiongling Mochizuki, Takuro Differential Geometry Complex Variables 53C07, 58E15 This paper is the second part of our study on the Toda equations and the cyclic Higgs bundles associated to $r$-differentials over non-compact Riemann surfaces. We classify all the solutions up to boundedness around the isolated singularity of an $r$-differential under the assumption that the $r$-differential is meromorphic or has some type of essential singularity. As a result, for example, we classify all the solutions on ${\mathbb C}$ if the $r$-differential is a finite sum of the exponential of polynomials. |
| title | Isolated singularities of Toda equations and cyclic Higgs bundles |
| topic | Differential Geometry Complex Variables 53C07, 58E15 |
| url | https://arxiv.org/abs/2010.06129 |