Timeline for coherent sheaves
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2012 at 11:44 | comment | added | Qfwfq | * Sorry, I meant: $h_1=1_{\mathcal{O}_X}$. | |
| Nov 21, 2012 at 11:43 | comment | added | Qfwfq | I think the question -as it stands now- is not well phrased. For example you give no compatibility conditions on the $U_i\cap U_j$. What if $X=\mathbb{A}^1$, $k=2$, $U_1=U_2=\mathbb{A}^1$, $F=G=\mathcal{O}_X$, $h_1=\mathrm{id}_X$, $h_2=0$ ? | |
| Nov 21, 2012 at 11:17 | comment | added | Sasha | This is true if $F$ is locally free (and $G$ can be arbitrary, smoothness of $X$ is not important either) and if morphisms $h_i$ agree on intersections $U_i \cap U_j$. To prove replace $Hom(F,G)$ by $H^0(X,F^*\otimes G)$. | |
| Nov 21, 2012 at 11:06 | history | asked | joy | CC BY-SA 3.0 |