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.

我们从滑轮理论的角度研究Fuchsian连接的单峰减少，重点是解决了具有四个奇点的特殊连接的奇点的情况。研究的主要工具是基于Drinfeld和Oblezin的束修改技术。这种通过不变空间和特征值问题的方法不仅使我们能够解释Erdélyi对Heun方程解的经典无限超几何展开，而且可以得到他的论文中未发现的新展开。结果，获得了武村特征值包含定理的几何证明。最后，我们观察到了单峰简化准则之间的精确匹配，这些准则给出了Heun方程的那些特殊解和给出了PainlevéVI方程的经典解。