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In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, either real or complex, in a projective space, thereby realizing it as a projective algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th exterior power of . The image is algebraic, consisting of the intersection of a number of quadrics defined by the § Plücker relations.
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