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Grassmann bundle

In algebraic geometry, the Grassmann d-plane bundle of a vector bundle E on an algebraic schemeX is a scheme over X: p:Gd(E)→X{\displaystyle p:G_{d}(E)\to X}such that the fiber p−1(x)=Gd(Ex){\displaystyle p^{-1}(x)=G_{d}(E_{x})} is the Grassmannian of the d-dimensional vector subspaces of Ex{\displaystyle E_{x}}.

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