Abstract
We prove that some holomorphic functions on the moduli space of tori have only simple zeros. Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Painlevé VI equation. As an application of this simple zero property, we obtain the smoothness of the degeneracy curves of trivial critical points for some multiple Green function.
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Acknowledgements
The first author was supported by National Natural Science Foundation of China (Grant No. 11701312). The authors thank Chin-Lung Wang very much for providing the file of Figure 1 to them.
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Dedicated to Professor Lo Yang on the Occasion of His 80th Birthday
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Chen, Z., Kuo, TJ. & Lin, CS. Simple zero property of some holomorphic functions on the moduli space of tori. Sci. China Math. 62, 2089–2102 (2019). https://doi.org/10.1007/s11425-018-9355-0
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DOI: https://doi.org/10.1007/s11425-018-9355-0