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 Pain...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.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11701312)
文摘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.
