Timeline for Examples of non-Kahler compact symplectic manifolds.
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 12:22 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Sep 22, 2012 at 15:49 | comment | added | Tim Perutz | It seems interesting to ask what happens if you take e.g. some Noether-violating simply connected symplectic 4-manifold and build a symplectic 8-manifold by this procedure; can it ever be Kaehler? | |
| Sep 22, 2012 at 15:45 | comment | added | Tim Perutz | Agol: in step 1, the symplectic mapping torus $X$ is $S^1$ times the usual one. A general theorem of Gromov-Tischler embeds the resulting (integral) symplectic $2N$-manifold symplectically into $\mathbb{C}P^{2N+1}$. You can blow up along such a submanifold much as you would in Kaehler geometry (see e.g Voisin's book). If $b_1(X)$ is odd, we get a symplectic $2N$-manifold with odd $b_3$. Donaldson hypersurfaces obey the Lefschetz hyperplane theorem, so you can then cut down to 8 dimensions preserving the odd $b_3$. | |
| Sep 22, 2012 at 1:24 | comment | added | Ian Agol | could you add some details or references - how are you blowing up? why are the Donaldson hypersurfaces not Kahler? | |
| Sep 21, 2012 at 23:48 | history | answered | eigenbunny | CC BY-SA 3.0 |