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Grassmannians are algebraic varieties whose points corresponds to vector subspaces of a fixed dimension in a fixed vector space.

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Vector bundles on Stein manifolds

This might be standard if true (if so, I shall be grateful if provided with a reference). Given a smooth map from a Stein manifold $X$ to $\operatorname{Gr}(k,n)$ (the Grassmannian of $k$ planes in $\ …