Timeline for Minimal model which is necessarily singular
Current License: CC BY-SA 2.5
11 events
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| Apr 24, 2010 at 1:43 | history | undeleted | VA. | ||
| Apr 23, 2010 at 4:09 | history | deleted | VA. | ||
| Apr 13, 2010 at 16:37 | comment | added | VA. | Andrea: yes, my comment was ironic. I think I understand what you are after: an example of a smooth 3-fold for which $h^0(nK_Y)$ grows like $dn^3/3!$ with $d=1/2$ or some other fractional number. I gave you such an example indirectly; you want something where the statement could be checked easily, without 3-fold theory. Oh well, a search of some didactic papers by Miles Reid may yield such an example. Good luck. | |
| Apr 13, 2010 at 9:19 | comment | added | quim | I think VA's accepts it is dangerous to "know the singularities which appear," not that his knowledge of the theory is dangerous. | |
| Apr 13, 2010 at 8:33 | comment | added | Andrea Ferretti | I sincerely don't understand your ironic comment. I have asked for an intersection-theoretic argument and you gave a different one. So I have asked for something different. There must be some motivation to introduce canonical, terminal singualrities and so on. So it would be nice to see this example BEFORE learning the machinery you mention (which, by the way, I more or less know). As I said above, it is not even a priori obvious that the right setting for the MMP must include singular varieties, for instance for surfaces this is not true. | |
| Apr 12, 2010 at 20:39 | comment | added | VA. | I agree, knowledge is a dangerous thing to have. | |
| Apr 12, 2010 at 18:13 | comment | added | Andrea Ferretti | I don't think this answer is in the same spirit, since it assumes one already knows about the singularities which appear in the MMP. Instead, the example I'm thinking of can actually be used to motivate the idea that one cannot do the MMP in the smooth setting (but not all singularities can be accepted, since one needs some intersection theory to say that the canonical is nef). | |
| Apr 12, 2010 at 15:44 | history | edited | VA. | CC BY-SA 2.5 |
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| Apr 12, 2010 at 13:57 | history | edited | VA. | CC BY-SA 2.5 |
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| Apr 12, 2010 at 13:49 | history | edited | VA. | CC BY-SA 2.5 |
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| Apr 11, 2010 at 15:30 | history | answered | VA. | CC BY-SA 2.5 |