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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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Sheaf of Sections of Cone

Fulton's intersection theory book at Chapter 4 makes the following claim: If $\mathcal{E}$ is a locally free sheaf (on $X$), and $E:=Spec(Sym(\mathcal{E}))$ a total space of some cone/bundle on $X$, t …