Timeline for How to descend a line bundle from the normalization of a surface?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 30, 2016 at 7:36 | comment | added | Laurent Moret-Bailly | See Th 2.2 in D. Ferrand, Bull. Soc. Math. France 131 (4) 2003, 553-585. | |
| Jul 30, 2016 at 5:36 | comment | added | Sasha | Imagine you defined sheaf $L$ by your sequence. Since locally $\mathcal{L} \cong O_{\tilde{S}}$, it follows that locally $L \cong O_S$, hence is a line bundle. | |
| Jul 29, 2016 at 20:43 | comment | added | Emre | There is such an exact sequence, but we tweaked the quotient map. $O_S$ itself gives the obvious isomorphism between the two pullbacks $\sigma_i^* O_{\tilde S}$, taking $1 \mapsto 1$. I am essentially asking if I glue using $1 \mapsto c$ for some $c \in k$ will I still get a line bundle. | |
| Jul 29, 2016 at 20:18 | comment | added | Sasha | The question is local, so it is enough to show that there is an exact sequence $0 \to O_S \to \nu_*O_{\tilde{S}} \to \sigma_{2*}O_{C_2} \to 0$. | |
| Jul 29, 2016 at 20:01 | history | asked | Emre | CC BY-SA 3.0 |