Timeline for Is there an Oka-Grauert principle for homogeneous spaces?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 23, 2014 at 12:18 | history | edited | Matthias Wendt | CC BY-SA 3.0 |
fixed spelling and grammar
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| Nov 23, 2014 at 10:32 | answer | added | Matthias Wendt | timeline score: 6 | |
| Nov 22, 2014 at 21:24 | comment | added | Jason Starr | I believe Grauert-Oka does apply to a holomorphic fibration by projective homogeneous spaces over the punctured disk. The family is equivalent to a holomorphic principal bundle for complex Lie group of biholomorphisms of the projective homogeneous space, and you can apply Grauert-Oka to this principal bundle. For a Fano fibration, the same holds if you know that every fiber is biholomorphic (again reduce to a principal bundle for the biholomorphism group of the Fano). Some of this is discussed in my paper, "Discriminant Avoidance..." with de Jong. | |
| Nov 22, 2014 at 18:28 | comment | added | Matthias Wendt | The question does not seem to have anything to do with the Oka-Grauert principle mentioned in the title... If you are trying to get a holomorphic section by applying the Oka-Grauert principle to a topological section, then you probably want "fibration" to mean subelliptic submersion and consult Forstneric's book "Stein manifolds and holomorphic mappings". | |
| Nov 22, 2014 at 17:42 | answer | added | abx | timeline score: 3 | |
| Nov 22, 2014 at 17:01 | comment | added | Ben McKay | Ngaiming Mok has done some relevant work. There are nontrivial examples where all fibers away from the central fiber are isomorphic and the central fiber is something topologically different, even for homogeneous Fano manifolds. | |
| Nov 22, 2014 at 15:49 | history | asked | user42804 | CC BY-SA 3.0 |