Timeline for What is the relation between vector bundles on a manifold and grassmanians?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2010 at 0:00 | comment | added | BCnrd | Thaaat's all, folks. | |
| Jul 20, 2010 at 21:00 | history | edited | Bugs Bunny | CC BY-SA 2.5 |
added 20 characters in body
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| Jul 20, 2010 at 13:59 | comment | added | BCnrd | Probably replace $V_p$ with $\wedge^m(V)_p$ in both places. But then this is all about $\wedge^m(V)$, and $V$ has sort of dropped out of the picture. So one doesn't see a Plucker map in this picture. But if $V$ is generated by $n$ global sections (no need for holomorphic structure or finite-dim. hypotheses), the quotient map $O^n \rightarrow V$ gives a map to a Grassmannian, and then composing with a Plucker embedding gives a map to a projective space, resting on the rank-1 quotient $\wedge^m(O^n) \rightarrow \wedge^m(V)$ (and then one can bring in ampleness considerations, etc.). | |
| Jul 20, 2010 at 10:25 | history | answered | Bugs Bunny | CC BY-SA 2.5 |