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9 votes

What functor does Grassmannian represent?

Let me elaborate on some of the other answers. On the Grassmannian X = Gr(k,n) (I am using this notation to mean k-dimensional subspaces of an n-dimensional vector space), we have the trivial bundle …
Ilya Nikokoshev's user avatar
5 votes
Accepted

What functor does a Schubert variety represent?

Everything you said should be fine. As for the case of not necessarily reduced schemes, we have to be careful, but I think the following will work. Say E is our given vector bundle of rank n which i …
Steven Sam's user avatar
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