Timeline for pushforward of locally free sheaf is locally free?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2020 at 0:39 | comment | added | Chan Ki Fung | Why nontrivial extension implies that $f_*E$ is not locally free? Suppose you have an extension $0\to k \to M \to k \to 0$ of $k[\epsilon]$ module. I think $M=k\oplus k$ when then extension is trivial, and $M=k[\epsilon]$ when it isn't. | |
| Sep 29, 2011 at 5:16 | comment | added | naf | Line bundles on $C_{\epsilon}$ with a trivialisation over $C$ correspond bijectively to $Ext^1_C(\mathcal{O}_C,\mathcal{O}_C) = H^1(C, \mathcal{O}_C)$. This identification is given precisely by the boundary map, so a line bundle is trivial iff the corresponding boundary map is zero. | |
| Sep 28, 2011 at 19:37 | comment | added | Nicolás | Thanks for the answer. Why is the boundary map nonzero? | |
| Sep 28, 2011 at 19:35 | vote | accept | Nicolás | ||
| Sep 28, 2011 at 5:19 | history | answered | naf | CC BY-SA 3.0 |