Timeline for Complex conjugation inducing a trivial map on the fundamental group
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2020 at 17:54 | comment | added | user145520 | @PiotrAchinger I thought it was not research-level | |
| Jun 30, 2020 at 16:06 | comment | added | Piotr Achinger | @vrz why did you delete another question of yours after I answered it in the comments? | |
| Jun 29, 2020 at 0:06 | comment | added | Ben Wieland | Where are going to get variety over $\mathbb C$ with fundamental group $G$? Have you heard of Godeaux-Serre varieties? I think that if you just follow the construction over $\mathbb R$, you get what you seek. I googled Godeaux-Serre to see if there was a useful reference, and I didn't find one. But I did find this paper saying that you can have whatever action you want, over any field. | |
| Jun 28, 2020 at 19:20 | history | edited | user145520 | CC BY-SA 4.0 |
deleted 4 characters in body
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| Jun 27, 2020 at 23:54 | comment | added | Ian Agol | You might be able to concoct an example from a finite group representation. Suppose one has a complex representation which is conjugation equivariant, so that conjugation acts nontrivially. The action on a Flag variety should give a complex projective variety with the appropriate properties I think. | |
| Jun 27, 2020 at 12:08 | history | edited | user145520 | CC BY-SA 4.0 |
added 34 characters in body
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| Jun 26, 2020 at 12:34 | comment | added | Donu Arapura | Don't forget about base points. Usually it can be ignored, but in this case, you probably need to pick one in $V(\mathbb{R})$. In particular, the set of real points should be nonempty. | |
| Jun 25, 2020 at 20:43 | comment | added | user145520 | @PiotrAchinger I forgot to add a condition | |
| Jun 25, 2020 at 20:42 | history | edited | user145520 | CC BY-SA 4.0 |
added 27 characters in body
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| Jun 25, 2020 at 20:30 | comment | added | Piotr Achinger | How does conjugation act on $V$ or $G$? | |
| Jun 25, 2020 at 20:25 | history | asked | user145520 | CC BY-SA 4.0 |