Timeline for Is the generic deformation of a symplectic variety affine?
Current License: CC BY-SA 2.5
7 events
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| Dec 14, 2010 at 6:58 | comment | added | Ben Webster♦ | It's not stated explicitly in the paper I referenced, but I see now that it is clear from the existence and properties of the twistor deformation. | |
| Dec 13, 2010 at 0:24 | comment | added | Misha Verbitsky | In this case, it is affine, but I don't know a precise reference. I think it is due to Kaledin. I am surprised it's not stated in the paper you cited. For an easy proof, notice that your C^*-action gives a C^*-action with positive weights on a deformation of your original (singular) affine manifold. Therefore the total space of its deformation (which has the same generic fibers as the hyperkaehler deformation of its blow-up) is affine, hence its fibers are affine, too. | |
| Dec 12, 2010 at 21:17 | comment | added | Ben Webster♦ | Though, I suppose it's worth asking: in the situations I'm interested in, the variety $X$ has a $\mathbb{C}^*$-action which is dilating on the affinization (as defined in arxiv.org/pdf/math/0608143.pdf), and thus I can try to put an algebraic structure $\tilde X$ by making weight vectors algebraic. Do you know if that will give the deformation an algebraic structure for which it is generically affine? | |
| Dec 12, 2010 at 20:44 | comment | added | Ben Webster♦ | That's a very useful answer. Thanks a lot. | |
| Dec 12, 2010 at 20:42 | vote | accept | Ben Webster♦ | ||
| Dec 12, 2010 at 20:37 | history | edited | Ben Webster♦ | CC BY-SA 2.5 |
added 2 characters in body
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| Dec 12, 2010 at 19:26 | history | answered | Misha Verbitsky | CC BY-SA 2.5 |