Solution to SU(n+1) Toda system generated by spherical metrics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917213044211712 |
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| author | Shi, Yiqian Wei, Chunhui Xu, Bin |
| author_facet | Shi, Yiqian Wei, Chunhui Xu, Bin |
| contents | Using the correspondence between solutions to the SU(n+1) Toda system on a Riemann surface and totally unramified unitary curves, we show that a spherical metric $ω$ generates a family of solutions, including $(i(n+1-i)ω)_{i=1}^n$. Moreover, we characterize this family in terms of the monodromy group of the spherical metric. As a consequence, we obtain a new solution class to the SU(n+1) Toda system with cone singularities on compact Riemann surfaces, complementing the existence results of Lin-Yang-Zhong (JDG, 114(2):337-391, 2020). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solution to SU(n+1) Toda system generated by spherical metrics Shi, Yiqian Wei, Chunhui Xu, Bin Mathematical Physics Using the correspondence between solutions to the SU(n+1) Toda system on a Riemann surface and totally unramified unitary curves, we show that a spherical metric $ω$ generates a family of solutions, including $(i(n+1-i)ω)_{i=1}^n$. Moreover, we characterize this family in terms of the monodromy group of the spherical metric. As a consequence, we obtain a new solution class to the SU(n+1) Toda system with cone singularities on compact Riemann surfaces, complementing the existence results of Lin-Yang-Zhong (JDG, 114(2):337-391, 2020). |
| title | Solution to SU(n+1) Toda system generated by spherical metrics |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2501.08132 |