Let $G$ be a reductive affine algebraic group defined over $\mathbb{C}$, and let $\nabla_0$ be a meromorphic $G$-connection on a holomorphic principal $G$-bundle $E_0$, over a smooth complex projective curve $X_0$, with polar locus $P_0 \subset X_0$. We assume that $\nabla_0$ is irreducible in the sense that it does not factor through some proper parabolic subgroup of $G$. We consider the universal isomonodromic deformation $(E_t \to X_t ,\nabla_t , P_t)_{ t\in \mathcal{T}}$ of $(E_0 \to X_0 ,\nabla_0, P_0)$, where $\mathcal{T}$ is a certain quotient of a certain framed Teichmüller space we describe. We show that if the genus $g$ of $X_0$ satisfies $g \geq 2$, then for a general parameter $t \in \mathcal{T}$, the principal $G$-bundle $E_t \to X_t$ is stable. For $g \geq 1$, we are able to show that for a general parameter $t \in \mathcal{T}$, the principal $G$-bundle $Et \to X_t$ is semistable.

中文翻译：

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不规则连接的等单变形和束的稳定性

设$ G $为在$ \ mathbb {C} $上定义的归约仿射代数组，并让$ \ nabla_0 $为全纯本金$ G $-束$ E_0 $上的亚纯$ G $-连接，复杂的投影曲线$ X_0 $，极坐标为$ P_0 \子集X_0 $。我们假设$ \ nabla_0 $是不可约的，因为它不会通过$ G $的某个适当抛物线子组进行分解。我们考虑等价的普遍等单变形$（E_t \ to X_t，\ nabla_t，P_t）_ {t \ in \ mathcal {T}} $ of $ {E_0 \ to X_0，\ nabla_0，P_0）$，其中$ \ mathcal { T} $是我们描述的特定框架Teichmüller空间的特定商。我们表明，如果$ X_0 $的属$ g $满足$ g \ geq 2 $，则对于通用参数$ t \ in \ mathcal {T} $，本金$ G $-束$ E_t \ to X_t $是稳定的。对于$ g \ geq 1 $，我们可以证明，对于\ mathcal {T} $中的常规参数$ t \，