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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.

5 votes
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162 views

Flatness of Chern classes for flat family of sheaves

Let $Q$ be a quasi-projective $k$-scheme (not necessarily smooth), $X$ a smooth projective $k$-variety and $\mathcal E$ a family of (torsion free) sheaves on $X$ parametrized by $Q$. Suppose that $\ma …