Timeline for Non-compact complex surfaces which are not Kähler
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2012 at 13:57 | vote | accept | Michael Albanese | ||
| Feb 21, 2012 at 0:39 | comment | added | YangMills | @Gunnar: you might also know about Inoue surfaces, which are compact complex non-Kahler surfaces of class VII with $b_2=0$, and which have no complex curves. Higher-dimensional versions of Inoue surfaces are the Oeljeklaus-Toma manifolds, which are non-Kahler and also have no closed complex subvarieties other than points, see arXiv.org/abs/1009.1101 | |
| Feb 20, 2012 at 21:59 | comment | added | Gunnar Þór Magnússon | @diverietti: How sure are we about that "often"? The main examples of non-Kahler manifolds - Hopf manifolds and the Iwasawa manifold - are torus fibrations and thus contain submanifolds. The only examples I know of manifolds that contain no submanifolds are general tori and certain hyperkahler manifolds, and both are Kahler. | |
| Feb 20, 2012 at 18:27 | history | edited | Donu Arapura | CC BY-SA 3.0 |
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| Feb 20, 2012 at 17:44 | comment | added | diverietti | the point is that often a non-kähler, and hence non-projective, manifold does not have any closed submanifold at all... so the hopf surface is a quite particular case... | |
| Feb 20, 2012 at 17:34 | comment | added | Elizabeth S. Q. Goodman | Oh right--so, no $\omega$-positive curves in an exact symplectic manifold, in particular the 2nd-homology obstruction still is useful for closed curves in an open Kähler manifold. Nice. | |
| Feb 20, 2012 at 16:53 | comment | added | diverietti | Very very nice! | |
| Feb 20, 2012 at 14:30 | history | answered | Donu Arapura | CC BY-SA 3.0 |