论文标题
解决奇异性和减少紫红色连接的单轨道
Resolving singularities and monodromy reduction of Fuchsian connections
论文作者
论文摘要
我们研究了从滑轮的理论观点中减少紫红色连接的单轨道，重点是解决与四个奇点的特殊连接的奇异性。研究的主要工具是{基于}由于Drinfeld和Oblezin引起的束修改技术。通过不变空间和特征值问题这种方法，我们不仅可以解释Erdélyi的经典无限的无限高几何扩展对Heun方程式的解决方案，而且还可以获得他在论文中找不到的新扩展。结果，获得了Takemura特征值纳入定理的几何证明。最后，我们观察到单一减少标准之间的精确匹配，从而提供了特殊的Heun方程解决方案，并提供了PainlevéVI方程的经典解。
We study monodromy reduction of Fuchsian connections from a sheave theoretic viewpoint, focusing on the case when a singularity of a special connection with four singularities has been resolved. The main tool of study is {based on} a bundle modification technique due to Drinfeld and Oblezin. This approach via invariant spaces and eigenvalue problems allows us not only to explain Erdélyi's classical infinite hypergeometric expansions of solutions to Heun equations, but also to obtain new expansions not found in his papers. As a consequence, a geometric proof of Takemura's eigenvalues inclusion theorem is obtained. Finally, we observe a precise matching between the monodromy reduction criteria giving those special solutions of Heun equations and that giving classical solutions of the Painlevé VI equation.
