Timeline for Number of connected components of an Automorphism group
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18, 2017 at 21:20 | comment | added | Uri Bader | Relevant: mathoverflow.net/q/8812/89334 | |
| Apr 17, 2017 at 15:27 | comment | added | Uri Bader | I have a certain confidence in the claim that the automorphism group of an affine variety is an ind-group, though I have never checked the details. However, I am 100% sure that it is an ind-variety, which is enogh for the required countability result. I happened to explain this recently in mathoverflow.net/a/266803/89334. It seems reasonable to extend this to arbitrary varieties. | |
| Apr 17, 2017 at 14:10 | answer | added | Jason Starr | timeline score: 3 | |
| Apr 17, 2017 at 13:33 | comment | added | YCor | I've found several claims by H. Kraft that the automorphism group of an affine variety is an ind-group (which implies this countability result), with reference to a paper in preparation with Furter. I don't know if some unexpected difficulty explains that the paper is not available now, nor if there is any reason not to expect that this holds in more generality, namely for arbitrary quasi-projective varieties (which certainly would be more technical to prove). | |
| Apr 17, 2017 at 11:21 | comment | added | YCor | If I'm optimistic, I'd expect that there's a reasonable notion of degree such that automorphisms of degree $\le n$ form a variety (or something not so far from a variety) and hence would map to only a finite subset of $Q(X)$, which would entail the countability result. In case $X$ is affine it's easy to check working with coordinate rings. | |
| Apr 17, 2017 at 10:32 | history | edited | Anonymous | CC BY-SA 3.0 |
corrected the definition of Aut(X)^0
|
| Apr 17, 2017 at 9:57 | history | asked | Anonymous | CC BY-SA 3.0 |