Timeline for Zero-cohomology of birational varieties
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2013 at 7:57 | comment | added | Laurent Moret-Bailly | As you define it, $f_*$ depends on the choice of $U_1$. | |
| Feb 19, 2013 at 0:16 | vote | accept | Joaquín Moraga | ||
| Feb 18, 2013 at 23:54 | comment | added | Sándor Kovács | OK, so this is much better. Of course, now the answer you accepted does not answer your question. Which makes me wonder what you had in mind when you accepted it. Sasha did not know what you really asked so he answered what he assumed you did, but you should have realized that. I'm sorry to be so critical, but I feel that if we invest time and energy to answer questions, it is a reasonable expectation that the person asking the question would do the same. | |
| Feb 18, 2013 at 23:50 | answer | added | Sándor Kovács | timeline score: 3 | |
| Feb 18, 2013 at 19:37 | history | edited | Joaquín Moraga | CC BY-SA 3.0 |
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| Feb 18, 2013 at 19:35 | comment | added | Joaquín Moraga | Thanks for the sugesstions Artie and Sándor. I edited some of the mistakes. | |
| Feb 18, 2013 at 19:31 | history | edited | Joaquín Moraga | CC BY-SA 3.0 |
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| Feb 18, 2013 at 19:05 | comment | added | user5117 | the solid arrow $\rightarrow$ to denote a rational map, but often that symbol is reserved for morphisms, and a broken arrow $\dashrightarrow$ is used for rational maps. As a result, it was easy to think that $f$ in your question was supposed to be a morphism. (Likewise, the notation $f_∗$ can be ambiguous, as Sándor pointed out.) Anyway, these are just some ideas about what would have made the question easier to understand for me. Best wishes, Artie. | |
| Feb 18, 2013 at 18:53 | comment | added | user5117 | Dear Joaquin, let me add a bit to Sándor's suggestions above. It might be a good idea to describe the situation you're interested in, in more detail. For example, you write "any divisor D in Pic(X)", which suggests that maybe you only want to consider smooth varieties X and Y. (Of course I might be wrong about that.) Even if the question admits an answer in greater generality, it is often better to start off in this more specific setting, to avoid confusions of the kind that arose. Another tip is to be very careful when using notation that has multiple meanings: you used... | |
| Feb 18, 2013 at 17:24 | comment | added | Sándor Kovács | @Joaquin: this is still a total mess. You should assume that $Y$ is at least $S_2$ and explain what you mean by $f_*$ if $f$ is not necessarily a morphism. Supposedly you want the strict transform of the divisor, but we shouldn't be guessing what you are asking. Also, $h^0(D)$ makes no sense if $D$ is a divisor and not a sheaf. Finally, $\mathrm{Pic} X$ is a set/group of sheaves not divisors: $D\in\mathrm{Pic} X$ is still a sheaf and not a divisor even if you call it a divisor. If you want help, at least invest enough energy to put the question together in a semi-intelligent way. | |
| Feb 18, 2013 at 17:14 | comment | added | Joaquín Moraga | $f$ is a birational map, not necessarily a morphism. $f_*$ is the push-forwards homomorphism. | |
| Feb 18, 2013 at 17:08 | history | edited | Joaquín Moraga | CC BY-SA 3.0 |
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| Feb 18, 2013 at 17:05 | vote | accept | Joaquín Moraga | ||
| Feb 19, 2013 at 0:16 | |||||
| Feb 18, 2013 at 17:05 | vote | accept | Joaquín Moraga | ||
| Feb 18, 2013 at 17:05 | |||||
| Feb 18, 2013 at 14:28 | comment | added | user5117 | Let me ask for clarification: is $f$ a morphism or just a map? | |
| Feb 18, 2013 at 8:09 | answer | added | Sándor Kovács | timeline score: 0 | |
| Feb 18, 2013 at 7:42 | comment | added | Sándor Kovács | This is a weird question. How do you define $f_*$ without knowing the answer to this? | |
| Feb 18, 2013 at 5:49 | vote | accept | Joaquín Moraga | ||
| Feb 18, 2013 at 17:05 | |||||
| Feb 18, 2013 at 5:47 | answer | added | Sasha | timeline score: 2 | |
| Feb 18, 2013 at 3:38 | history | asked | Joaquín Moraga | CC BY-SA 3.0 |