Schubert variety

In algebraic geometry, a Schubert variety is a certain subvariety of a Grassmannian, of -dimensional subspaces of a vector space , usually with singular points. Like the Grassmannian, it is a kind of moduli space, whose elements satisfy conditions giving lower bounds to the dimensions of the intersections of its elements , with the elements of a specified complete flag. Here may be a vector space over an arbitrary field, but most commonly this taken to be either the real or the complex numbers.

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