Timeline for Three-dimensional compact Kähler manifolds
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 9, 2013 at 9:10 | comment | added | BS. | @Andrei : There are other obstructions known on the fundamental group see e.g. homepages.math.uic.edu/~jaca2009/notes/Arapura.pdf , plus, in the paper by Voisin you cite, her goal is to show that there are other obstructions, coming from the algebra structure of the cohomology. | |
| Jul 8, 2013 at 15:59 | comment | added | Gunnar Þór Magnússon | That is very probably not sufficient. Consider Hironaka's example $X$ of a non-Kahler deformation of projective manifolds. That manifold is Moishezon since it is a deformation limit of projective manifolds (by Popovici, I think). Then there exists a modification $\epsilon X \to X'$ where $X'$ is projective. It follows that the cohomology ring of $X$ admits a Hodge decomposition. I would think that you could then find some $(1,1)$-class on $X$ to play the role of a Kahler class in the hard Lefschetz theorem, the only difference being that it wouldn't be represented by a Kahler form. | |
| Jul 8, 2013 at 9:30 | history | answered | Andrei Halanay | CC BY-SA 3.0 |