Simple zero property of some holomorphic functions on the moduli space of tori

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（11）
• 页码范围: 2089-2102
• 页数: 14页
• 语种: 英文

摘要

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 7,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.