Timeline for Iterated extensions of quotients of vector bundles
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2014 at 15:19 | comment | added | Olivier Benoist | @MartinBrandenburg : my point is that it might be expected that $\mathcal{S}=Coh(X)$ under mild hypotheses. If this is the case, your conditions (ii), (iii), (iv) do not prevent you from having to construct vector bundles to prove it. I am sorry if what I meant was not clear in my answer. | |
| Mar 7, 2014 at 14:33 | comment | added | Martin Brandenburg | "For this reason, to answer your question, you have to find a way to construct non-trivial vector bundles" I don't fully agree. In your example, there are enough vector bundles. Of course there are schemes on which every vector bundle is trivial, but there one has to determine $\mathcal{S}$ then. | |
| Mar 7, 2014 at 14:27 | comment | added | Jason Starr | Just to add one supporting comment to Olivier's answer: consider the case when $X$ is $\mathbb{P}^n$ with a nontrivial double structure, as in Exercise III.5.9 of Hartshorne's "Algebraic Geometry". How do you know that there is any locally free sheaf other than $\mathcal{O}_X^{\oplus r}$? | |
| Mar 7, 2014 at 13:07 | history | answered | Olivier Benoist | CC BY-SA 3.0 |