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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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Composition of holomorphic maps and normal bundle

Blow up a point on a surface. The normal bundle of the projective line there will have a negative degree summand. Embed the surface in a projective space. The normal bundle of the projective line ther …
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