Timeline for Cone over the Veronese surface
Current License: CC BY-SA 3.0
22 events
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| Jan 8, 2015 at 10:00 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jan 8, 2015 at 6:59 | comment | added | Francesco Polizzi | Ok, now I completely agree with you. I (re)corrected the answer. Thanks. | |
| Jan 8, 2015 at 6:51 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jan 7, 2015 at 23:59 | comment | added | Sándor Kovács | I am sticking with $-5/2$, but not saying you're wrong. It's a question of what we're calling $\mathscr O_X(1)$. See my answer to your comment after my answer for more details. I think we agree in the essence of the result. | |
| Jan 7, 2015 at 20:50 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jan 7, 2015 at 20:39 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jan 7, 2015 at 20:30 | comment | added | Francesco Polizzi | By the way, I think that the final answer is $b/a = -5/1$, see my comment above. Cheers! | |
| Jan 7, 2015 at 20:27 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jan 7, 2015 at 20:07 | comment | added | Francesco Polizzi | Sandor, of course you are right. For some reason, I did not notice that my result was in contradiction with the rationality of $X$ :-) I've edited the answer. Thank you for correcting me (and HNY!) | |
| Jan 4, 2015 at 21:42 | vote | accept | CommunityBot | ||
| Jan 4, 2015 at 21:42 | |||||
| Jan 4, 2015 at 21:35 | vote | accept | CommunityBot | ||
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| Jan 2, 2015 at 21:16 | comment | added | Sándor Kovács | There is one more place to nitpick actually: In your final conclusion you are assuming that the Picard group of $X$ is torsion-free. This is of course true (see an easy argument in my answer) but perhaps deserves mentioning. Otherwise you only get that their ratio is $2:3$. Cheers! (and HNY!) | |
| Jan 2, 2015 at 21:15 | comment | added | Sándor Kovács | Francesco: This could not possibly be true. Your computation of $d$ shows that $X$ has terminal singularities, while $a,b>0$ implies that $X$ is canonically polarized, so that would imply that $Y$ is of general type. At the same time it is clearly rational. The error you made is very simple actually: I think that $K_Y\cdot \ell=-2$ and not $2$. Once you make that correction everything falls into place and you get the correct value $b/a=-5/2$. | |
| Jan 1, 2015 at 15:42 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 30, 2014 at 20:08 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 30, 2014 at 17:22 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 30, 2014 at 16:53 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 30, 2014 at 16:46 | history | undeleted | Francesco Polizzi | ||
| Dec 30, 2014 at 16:46 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 30, 2014 at 16:04 | history | deleted | Francesco Polizzi | via Vote | |
| Dec 30, 2014 at 16:04 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 30, 2014 at 15:38 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |