Let $X$ be a holomorphic vector bundle over $Y$. Y$ (where $Y$ is an arbitrary complex manifold, not necessary projective). Does there exist an analytic subset $Z$ of $Y$ such that the restriction of $X$ to $Y \setminus Z$ is a trivial vector bundle?
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non-trivial locus of a holomorphic vector bundleLet $X$ be a holomorphic vector bundle over $Y$. Does there exist an analytic subset $Z$ of $Y$ such that the restriction of $X$ to $Y \setminus Z$ is a trivial vector bundle?
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