Timeline for Serre vanishing on one-point blow-ups
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 21, 2020 at 4:14 | comment | added | Devlin Mallory | To see $R^1 \sigma_*\mathcal O_{\hat X}(-F)=0$: take $0\to \mathcal O_{\hat X}(-F)\to \mathcal O_{\widehat X}\to \mathcal O_F\to 0$, push it forward, and use that $\sigma_* \mathcal O_{\widehat X}=\mathcal O_X\to \sigma_* \mathcal O_F=\mathcal O_x$ is surjective and $R^1\sigma_* \mathcal O_{\hat X}=0$. | |
| Aug 21, 2020 at 4:12 | comment | added | Devlin Mallory | I think the following works: I think $R^1 \sigma_*\mathcal O_{\widehat X}(-F)=0$, so by the Leray--Serre spectral sequence and projection formula we have that the thing you're trying to show is 0 is equal to $H^1(E\otimes \sigma_*\mathcal O_{\widehat X}(-F)\otimes L^k)$; now using Serre vanishing on $X$ this is 0 for $k$ large. | |
| Aug 20, 2020 at 18:20 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
|
| Aug 20, 2020 at 16:29 | comment | added | Carlos Esparza | This question was migrated from math.SE | |
| Aug 20, 2020 at 16:29 | history | asked | Carlos Esparza | CC BY-SA 4.0 |