The generic element of the moduli space of logarithmic connections with parabolic points on holomorphic vector bundle over the Riemann sphere can be represented by a Fuchsian equation with some singularities and some apparent singularities. We analyze the case of rank 3 vector bundle which leads to third order Fuchsian equation. We find coordinates on an open subset of the moduli space and we construct a non-trivial part of the moduli space by blowing up along a variety in a special case.

中文翻译：

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用 Fuchsian 方程表示对数连接的轨迹

黎曼球面上与全纯向量丛上的抛物线点的对数连接模空间的一般元素可以由具有一些奇点和一些明显奇点的 Fuchsian 方程表示。我们分析了导致三阶 Fuchsian 方程的 3 阶向量丛的情况。我们在模空间的一个开放子集上找到坐标，并通过在特殊情况下沿变体放大来构建模空间的一个重要部分。