Timeline for Families of ideal sheaves: What's the correct definition?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2012 at 22:35 | comment | added | 36min | Now I'm more confused... In the Inventiones paper by Bridgeland, he really said "the scheme $M_I(X)$ is the moduli space of ideal sheaves on $X$". (See 7.3 of that paper.) He didn't say what that is and how it is constructed... I thought he meant some well-known thing. $M_I(X)$ is used in a crucial step which constructs another moduli space. | |
| Sep 18, 2012 at 19:19 | comment | added | Sándor Kovács | ...and that point is not closed! :) | |
| Sep 18, 2012 at 19:16 | comment | added | Sándor Kovács | OK, you guys have a point. I just tried to make sense of the issue.... | |
| Sep 18, 2012 at 19:15 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
deleted 92 characters in body; deleted 1 characters in body; added 61 characters in body
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| Sep 18, 2012 at 18:42 | comment | added | MartinG | @temp: No, $M_I(X)$ does not exist: it is not a functor. | |
| Sep 18, 2012 at 15:55 | comment | added | temp | Also, why does $M_I(X)$ exist as a scheme? It seems larger than $\text{Hilb}(X)$. Will there be any non-separatedness? It seems one can also define a similar scheme for Quot, namely one that classifies subsheaves which are flat over the base. Does that exist too? | |
| Sep 18, 2012 at 15:48 | comment | added | temp | What does the last sentence mean? How can two functors agree if they only agree on closed points, but not $S$-points? I think you pointed out they don't agree on $S$-points... Am I missing something? | |
| Sep 18, 2012 at 7:58 | history | answered | Sándor Kovács | CC BY-SA 3.0 |