Timeline for functor from semiorthogonal decomposition
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2013 at 7:49 | history | edited | Sasha | CC BY-SA 3.0 |
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| Dec 9, 2013 at 2:39 | comment | added | Aleksa | Where I can find something on that topic? I am searching for literature on how one can construct functors from glueing data as you pointed out above. | |
| Dec 9, 2013 at 2:32 | comment | added | Aleksa | Ok. Take for example $X=Y=\mathbb{P}^2$. We have semiorthogonal decomposition $D^b(X)=<\mathcal{O}_X,\mathcal{O}_X(1),\mathcal{O}_X(2)>$ and for $Y$ the same. And we consider equivalences $<\mathcal{O}_X(1)>\simeq <\mathcal{O}_Y(2)>$ and $<\mathcal{O}_X(2)>\simeq <\mathcal{O}_Y(1)>$. Can one may construct a functor compatible with the equivalences that may is a FM-functor? Under some assumptions this would give a birational map $X\rightarrow Y$ | |
| Dec 8, 2013 at 20:02 | comment | added | Sasha | If the gluing data is the same for both $D^b(X)$ and $D^b(Y)$ then (under appropriate technical assumptions) one can construct an equivalence of $D^b(X)$ and $D^b(Y)$. BTW, in this case it is automatically a FM-functor. | |
| Dec 8, 2013 at 19:19 | comment | added | Aleksa | Maybe the question is elementary but how can a glueing compatibility be involved in constructing a functor? Under what kind of assumptions on the glueing the resulting functor is a Fourier-Mukai transform? | |
| Dec 8, 2013 at 17:07 | history | answered | Sasha | CC BY-SA 3.0 |