We consider irreducible logarithmic connections $(E,\,\delta)$ over compact Riemann surfaces $X$ of genus at least two. The underlying vector bundle $E$ inherits a natural parabolic structure over the singular locus of the connection $\delta$; the parabolic structure is given by the residues of $\delta$. We prove that for the universal isomonodromic deformation of the triple $(X,\,E,\,\delta)$, the parabolic vector bundle corresponding to a generic parameter in the Teichm\"uller space is parabolically stable. In the case of parabolic vector bundles of rank two, the general parabolic vector bundle is even parabolically very stable.

中文翻译：

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对数连接和稳定抛物线向量丛的等单向变形

我们考虑不可约对数连接 $(E,\,\delta)$ 在至少两个属的紧致黎曼曲面 $X$ 上。底层向量丛$E$在连接$\delta$的奇异轨迹上继承了一个自然的抛物线结构；抛物线结构由 $\delta$ 的残差给出。我们证明对于三元组$(X,\,E,\,\delta)$的普遍等单向形变，Teichm\"uller空间中一个泛参对应的抛物线向量丛是抛物线稳定的。在对于二阶抛物线向量丛，一般抛物线向量丛甚至抛物线非常稳定。