Timeline for How much of a variety can be reconstructed from codimension-zero data?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Mar 29, 2013 at 4:36 | vote | accept | Dmitry Vaintrob | ||
| Mar 27, 2013 at 6:23 | comment | added | Jim Bryan | Can't we reconstruct $X$ as a component of the moduli space of objects of $\mathcal{C}$, namely the component parameterizing ideal sheaves of a point. | |
| Mar 25, 2013 at 19:15 | answer | added | Sasha | timeline score: 7 | |
| Mar 25, 2013 at 3:51 | comment | added | Will Sawin | My hunch is you are missing a lot in dimension $>1$. The reason is because the homs do not contain much global data: If $F$ is trivial outside $S$, and $G$ is trivial outside $T$, then on $X - S - T$, the $Hom(F,G)$ is just a vector space of dimension $dim (f) \times dim(G)$. Adding in $S$ and $T$ can lead to increases and decreases in the dimension, but nothing that illuminates the global geometry of the situation. And higher homs do not tell you much more than $H^k(X,\mathcal O_X)$, which of course is not a complete set of invariants. | |
| Mar 24, 2013 at 17:46 | comment | added | Dmitry Vaintrob | Yes, of course (otherwise it'd be boring in dimension $>1$). | |
| Mar 24, 2013 at 15:42 | comment | added | Sasha | How do you define $Hom$'s in your category? Is it a full subcategory of $Coh(X)$? | |
| Mar 24, 2013 at 14:40 | history | asked | Dmitry Vaintrob | CC BY-SA 3.0 |