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A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.

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Dimension of Quot scheme of zero dimensional quotients of a locally free sheaf

Your dimension is correct, this and more can be found in this article.
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2 votes
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Canonical (tautological) section of a family of sheaves

A couple of months ago, i saw a construction, that somehow looks like the construction of the tautological section of the pullback of a vector bundle to its total space, i am trying to piece it togeth …
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