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arXiv · 2501.08132

Solution to SU(n+1) Toda system generated by spherical metrics

Yiqian Shi·Chunhui Wei·Bin Xu
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Abstract

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 $\omega$ generates a family of solutions, including $(i(n+1-i)\omega)_{i=1}^n$. 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).

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Yiqian Shi, Chunhui Wei, Bin Xu. 2025-01-14. Solution to SU(n+1) Toda system generated by spherical metrics. https://doi.org/10.1016/j.jfa.2025.111197

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