We discuss the problem of lifting projective bundles to vector bundles, giving necessary and sufficient conditions for a lift to exist both in the smooth and in the holomorphic categories. These criteria are formulated and proved in the language of topology and complex differential geometry, respectively.

中文翻译：

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射影束的提升及其在弦流形上的应用

我们讨论了将射影束提升为矢量束的问题，并给出了在平滑和全纯类中存在提升的必要和充分条件。这些标准是分别用拓扑和复杂微分几何的语言制定和证明的。