Timeline for complex algebraic morphisms as topological maps: every morphism is a topological fibration on a Zariski dense open subset?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2013 at 9:19 | vote | accept | mmm | ||
| Feb 3, 2011 at 11:17 | comment | added | Daniel Loughran | The result in Hartshorne (Lemma 10.5) only assumes that you have a dominant morphism of integral schemes of finite type over an algebraically closed field of charactertistic zero. Indeed, in this case there is a open dense subset where your schemes are non-singular varieties. If the morphism is also proper then we can use Ehresmann's theorem to deduce that it is a fibration, but I guess you need more in the non-proper case. | |
| Feb 3, 2011 at 0:21 | comment | added | Donu Arapura | If the initial space is smooth, then yes, certainly. But it didn't seem that mmm was assuming this. | |
| Feb 2, 2011 at 22:43 | comment | added | Daniel Loughran | For (i) does "generic smoothness" not suffice? This is in Hartshorne, the chapter on smooth morphisms. | |
| Feb 2, 2011 at 18:44 | answer | added | Donu Arapura | timeline score: 5 | |
| Feb 2, 2011 at 15:29 | history | edited | mmm | CC BY-SA 2.5 |
edited title
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| Feb 2, 2011 at 12:54 | history | asked | mmm | CC BY-SA 2.5 |