Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $\varphi^* E$ is trivial for some surjective holomorphic map $\varphi$, to $M$, from some compact complex manifold. We prove that these are exactly those holomorphic vector bundles that admit a flat holomorphic connection with finite monodromy homomorphism. A similar result is proved for holomorphic principal $G$-bundles, where $G$ is a connected reductive complex affine algebraic group.

中文翻译：

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可通过真满射全纯映射平凡化的全纯束

给定一个紧复流形 $M$，我们研究了 $M$ 上的全纯向量丛 $E$，使得 $\varphi^* E$ 对于某些满射全纯映射 $\varphi$ 到 $M$ 是微不足道的，从一些紧凑复流形。我们证明这些正是那些承认与有限单态同态存在平面全纯连接的全纯向量丛。对全纯主$G$-bundles 证明了类似的结果，其中$G$ 是连通的还原复仿射代数群。