Timeline for Are conical symplectic resolutions Mori dream spaces?
Current License: CC BY-SA 3.0
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| Feb 7, 2013 at 23:27 | comment | added | user5117 | X/Y is a relative MDS, by BCHM. This is possible if Y is Q-factorial, as explained by Sandor here: mathoverflow.net/questions/86123/…. I don't know how much that helps with the original question, but I thought I'd mention it. | |
| Feb 7, 2013 at 23:22 | comment | added | user5117 | In case anyone still cares: I came across this question again because I was reading the paper of Andreatta--Wisniewski referred to by Ben. There they have a theorem (3.2) that all 4-dimensional symplectic contractions X -> Y are relative MDS, but I must admit I find their proof hard to follow. It uses the fact that X is symplectic, but not that much, it seems to me. So it seems as though one might be able to get somewhere with the original question using recent progress in MMP. More specifically, if one can find an effective Q-Cartier divisor on X which is anti-ample over Y, then... | |
| Nov 7, 2011 at 21:49 | comment | added | user5117 | I suspected the answer was something along those lines. Thanks for the clarification. | |
| Nov 7, 2011 at 21:02 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
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| Nov 7, 2011 at 21:01 | comment | added | Ben Webster♦ | Artie- I probably should have said "relative Mori dream space." Rather than a projective variety, I'm thinking about the projective map $X\to Y$. | |
| Nov 7, 2011 at 20:48 | comment | added | user5117 | Hi Ben, maybe a silly question: in my understanding (and the link you give) a Mori dream space is projective. But your examples are not all projective. What am I missing? | |
| Nov 7, 2011 at 17:05 | history | asked | Ben Webster♦ | CC BY-SA 3.0 |