Timeline for Zero-cohomology of birational varieties
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2013 at 23:56 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Feb 18, 2013 at 17:07 | comment | added | Joaquín Moraga | $D$ is a divisor, sorry for the confusion, i will edit it. | |
| Feb 18, 2013 at 16:20 | comment | added | Sasha | Undoubtedly, the question is very sloppy. But it seems that I was correct in guessing what the question was. | |
| Feb 18, 2013 at 16:11 | comment | added | Sándor Kovács | p.p.s.: In fact, how do you define the notion of a divisor under the assumptions? | |
| Feb 18, 2013 at 15:41 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Feb 18, 2013 at 15:21 | comment | added | Sándor Kovács | p.s.: By the way, if $D$ were a divisor, then WTH is $h^0(D)$? | |
| Feb 18, 2013 at 15:20 | comment | added | Sándor Kovács | That's what I thought first as the reasonable interpretation, but even though the OP used "$D$", he never said it was a divisor. The only stated property is that $D\in\mathrm{Pic} X$, which says it is a sheaf. Just because the OP uses a letter that's usually means divisors, it does not make it one. At best this is a very sloppy question. | |
| Feb 18, 2013 at 9:31 | comment | added | Sasha | The problem is that a priori the pushforward of a line bundle is not a line bundle. In other words, the pushforward of sheaves is not the same as the pushforward of divisors. | |
| Feb 18, 2013 at 8:40 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Feb 18, 2013 at 8:09 | history | answered | Sándor Kovács | CC BY-SA 3.0 |