射影结构、有理曲线的邻域与Painlev'e方程
经典分析与常微分方程
2021-06-18 v4 复变函数
微分几何
摘要
我们研究曲面上的局部（复解析）射影结构与具有自交+1的有理曲线的二维（复解析）邻域之间的对偶性。我们研究解析分类、正规形的存在性、束/纤维化分解、无穷小对称性。我们推导出关于Painlev'e方程的一些超越结果。
引用
@article{arxiv.1707.07868,
title = {Projective structures, neighborhoods of rational curves and Painlev'e equations},
author = {Maycol Falla Luza and Frank Loray},
journal= {arXiv preprint arXiv:1707.07868},
year = {2021}
}
备注
This version is a shortening of previous version v3. Some new results have been added, like prolongation of foliated structure in section 3.4, and non existence of foliated structure for many Painleve equations in section 6