Timeline for Extension between vector bundles inducing non-zero map on cohomology
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2021 at 1:24 | history | became hot network question | |||
| Apr 13, 2021 at 19:35 | vote | accept | SashaP | ||
| Apr 13, 2021 at 19:13 | answer | added | Will Sawin | timeline score: 5 | |
| Apr 13, 2021 at 19:10 | answer | added | Sasha | timeline score: 4 | |
| Apr 13, 2021 at 18:44 | comment | added | SashaP | @WillSawin Ah, good point, do you think that this could be salvaged if in place of $\mathcal{O}_X(d)$ we allow an arbitrary line bundle? (I've edited the question accordingly) | |
| Apr 13, 2021 at 18:43 | history | edited | SashaP | CC BY-SA 4.0 |
added 336 characters in body
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| Apr 13, 2021 at 18:12 | comment | added | Will Sawin | If $\mathcal O_X(1)$ is a line bundle of high enough degree on a curve, there could be no degrees where both those groups are nonvanishing (for $i=1$ in this case). But there are plenty of nontrivial Ext classes. For example $X = \mathbb P^1$, $E$ a line bundle of degree $1$, $F$ a line bundle of degree $-1$, and $\mathcal O_X(1)$ a line bundle of degree at least $2$. | |
| Apr 13, 2021 at 17:21 | history | asked | SashaP | CC BY-SA 4.0 |