Let X be a smooth complete complex toric variety such that the boundary is a simple normal crossing divisor, and let E be a holomorphic vector bundle on X. We prove that the following three statements are equivalent: \ud\udThe holomorphic vector bundle E admits an equivariant structure. \ud\udThe holomorphic vector bundle E admits an integrable logarithmic connection singular over D. \ud\udThe holomorphic vector bundle E admits a logarithmic connection singular over D. \ud\udWe show that an equivariant vector bundle on X has a tautological integrable logarithmic connection singular over D. This is used in computing the Chern classes of the equivariant vector bundles on X. We also prove a version of the above result for holomorphic vector bundles on log parallelizable G-pairs (X, D), where G is a simply connected complex affine algebraic group
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机译：令X为光滑的完整复曲面，使边界为简单的法线交叉除数，令E为X上的全纯矢量束。我们证明以下三个陈述是等价的：\ ud \ ud等变结构。 \ ud \ ud全纯向量束E接受D上的可积对数连接奇数\ ud \ ud全纯向量束E接受D上的对数连接奇数D上的连接奇异点。用于计算X上等变向量束的Chern类。我们还证明了对数可并行G对（X，D）上全纯向量束的上述结果的一种形式，其中G是单纯连通复仿射代数群
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