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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.

6 votes

Can $\mathbb{P}^n$ be regarded as an algebraic vector bundle over some algebraic variety?

That's right. I think the one sentence rephrasing of Kevin's argument would be proper morphisms are stable under pullback (this is obvious by the very definition of properness which is stated through …
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