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Results tagged with vector-bundles
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user 1784
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.
57
votes
Accepted
Why do Todd classes appear in Grothendieck-Riemann-Roch formula?
You look at the case when $X=D$ is a Cartier divisor on $Y$ (so that the relative tangent bundle -- as an element of the K-group -- is the normal bundle $\mathcal N_{D/X}=\mathcal O_D(D)$ (convenientl …
- 13.1k
38
votes
Accepted
Extending vector bundles on a given open subscheme
This is true if $X$ satisfies Serre's condition $S_2$, i.e. $\mathcal O_X$ is $S_2$. Then a vector bundle is $S_2$ since locally it is isomorphic to $\mathcal O_X^n$.
More generally, a coherent sheaf …
- 13.1k
17
votes
Accepted
Differences between reflexives and projectives modules
Well, the answer is well known of course. For a finitely generated module over a commutative normal Noetherian domain TFAE
M is reflexive
M is torsion-free and equals the intersection of its locali …
- 13.1k