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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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Singularities of hypersurfaces in projective bundles

I am doing some calculation on a toy example from the question here. Let $\mathbb P(E) \rightarrow \mathbb P^1$ be the projectization of the vector bundle $E = \mathcal O \oplus \mathcal O \oplus \ma …