奇异椭圆曲线的邻域与无穷远处的黎曼-希尔伯特对应
Neighborhoods of singular elliptic curves and the Riemann-Hilbert correspondence at infinity
- Univ Rennes, CNRS, IRMAR, UMR 6625（雷恩大学，法国国家科学研究中心，数学与随机模型研究组）
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AI总结：
本文研究奇异椭圆曲线邻域的解析分类，通过双重覆盖与光滑情形不变量关联，并推测其与Painlevé VI的无穷远黎曼-希尔伯特对应有关。
AI中文摘要：
在第一作者的学位论文工作中，他研究了Kodaira分类中$I_0^*$型奇异椭圆曲线的邻域，并给出了解析分类。这通过双重覆盖构造与Touzet、Voronin和第二作者为光滑椭圆曲线邻域的解析分类所发现的解析不变量相关联。在回顾这些构造之后，我们在本文中解释这一构造如何推测性地与Painlevé VI情形下Okamoto除子邻域考虑中的无穷远处黎曼-希尔伯特对应相关联。
英文摘要：
In his thesis work, the first author studies neighborhoods of singular elliptic curves of type $I_0^*$ (Kodaira's classification) and provides the analytic classification. This is related via a double covering construction to the analytic invariants found by Touzet, Voronin and the second author for the analytic classification of neighborhoods of smooth elliptic curves. After recalling these constructions, we explain in this note how this construction is conjecturally related to the Riemann-Hilbert correspondence at infinity for Painlev{é} VI case when considering neighborhood of Okamoto divisor.
