Timeline for Local structure of rational varieties
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2016 at 21:18 | answer | added | John Pardon | timeline score: 8 | |
| Jul 3, 2013 at 15:14 | history | edited | Charles Staats |
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| Jul 2, 2013 at 8:28 | answer | added | Francesco Polizzi | timeline score: 14 | |
| Oct 10, 2012 at 21:08 | comment | added | Jérémy Blanc | In dimension 2 the result is true and is in fact stronger: we can assume that the open neighbourhood is isomorphic to $\mathbb{A}^2$. Do you have a counterexample in dimension $3$ of this? By the way, I would have thought that the answer to your question (not the stronger one) should be "yes", but as many people think the converse, I am now confused. If a point admits no such neighbourhood, it implies that every birational maps $X\to \mathbb{P}^n$ is either not defined at $x$ or contracts something through $x$. Do you have some candidate for $x$ and $X$? | |
| Jun 9, 2012 at 6:59 | comment | added | Angelo | I remember discussing this with Joe Harris many years ago. The problem seems to have been around for a while. | |
| Jun 9, 2012 at 5:55 | comment | added | rita | Jason, thank you, this puts my question in perspective. | |
| Jun 8, 2012 at 21:52 | comment | added | Will Sawin | Trivial in dimension 1. True in dimension 2 because the minimal models have this property and blow-ups preserve it. Is it true in dimension 3? | |
| Jun 8, 2012 at 21:16 | comment | added | Jason Starr | I have discussed this over the years with several people. It is expected to be false, but it is open. | |
| Jun 8, 2012 at 20:40 | comment | added | user5117 | Qiaochu: every point. (I almost asked the same question, by the way.) | |
| Jun 8, 2012 at 20:32 | comment | added | Qiaochu Yuan | I don't understand. Isn't this true by definition? | |
| Jun 8, 2012 at 20:20 | history | asked | rita | CC BY-SA 3.0 |