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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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About universal Ext space
There is a natural action of $\operatorname{Hom}(L,Q)$ on $\operatorname{Ext}^1(L,Q)$, namely the trivial one.
There is a natural vector bundle stack over $J_{d_1}\times J_{d_2}$ whose fiber at eve …