Timeline for Semi-stable sheaves on quadric surface
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2021 at 8:37 | comment | added | Sasha | I think you will see this after performing the RR computation. | |
| Jun 9, 2021 at 8:31 | comment | added | H.S. Kim | Okay. By the way, how does this computation conclude $C_F \in |O_Q(n, m)|$? | |
| Jun 9, 2021 at 8:20 | comment | added | Sasha | Then substitute this into RR. | |
| Jun 9, 2021 at 7:41 | comment | added | H.S. Kim | Yes, I know that. | |
| Jun 9, 2021 at 7:15 | comment | added | Sasha | Do you know how a line bundle twist modifies the Chern character of a sheaf? | |
| Jun 9, 2021 at 6:47 | comment | added | H.S. Kim | I know RR. But how apply RR to compute $\chi$ of its twist? | |
| Jun 9, 2021 at 6:42 | comment | added | Sasha | What part of the explanation are you missing? Can you apply RR? | |
| Jun 9, 2021 at 6:22 | comment | added | H.S. Kim | @Sasha Thank you for the comment. However, I cannot understand your explanation since my lack of comprehension. Please explain above thing more detail. | |
| Jun 9, 2021 at 4:51 | comment | added | Sasha | This should follow from Riemann-Roch. Imagine that the sheaf is a rank 1 sheaf on a curve of type $(a,b)$, use RR to compute $\chi$ of its twists, and compare. So, the only problem is to show that its rank is 1 (it could be, say, a rank 2-sheaf on a curve of type $(n/2,m/2)$, or the curve could have several components and the sheaf could have different rank on different components), but this probably follows from other assumptions in the paper. | |
| Jun 9, 2021 at 4:32 | history | asked | H.S. Kim | CC BY-SA 4.0 |