Timeline for Computing the symmetric product of a sheaf supported on a divisor
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1 at 21:53 | comment | added | fool rabbit | @R.vanDobbendeBruyn Thanks for you answer, this is useful for me! | |
| Nov 1 at 21:10 | comment | added | R. van Dobben de Bruyn | Ah, in degree $0$ it will be $\mathcal O_X$, and in positive degree $n$ it will be $i_*i^*\mathscr L^{\otimes n}$. Indeed, what you have to check is that both $i^*$ and $i_*$ preserve tensor products. For $i^*$ this should be clear by definition, and for $i_*$ you use the local computation that $M \otimes_A N = M \otimes_{A/I} N$ if $M$ and $N$ are $A/I$-modules. (I'm assuming you mean that $\mathcal S$ is the symmetric algebra; please clarify if you mean something else.) | |
| Nov 1 at 19:56 | comment | added | fool rabbit | @R. van Dobben de Bruyn. Yes, I want know the form that is a infinty sum of $O_X$-module | |
| Nov 1 at 19:24 | comment | added | R. van Dobben de Bruyn | What does it mean for you to 'compute' this? It's already a pretty concrete thing, but maybe you're looking for an answer in some specific form? | |
| Nov 1 at 19:15 | history | asked | fool rabbit | CC BY-SA 4.0 |