Timeline for Why can I divide an affine variety by the action of the general linear group?

9 events

when toggle format	what		by	license	comment
Apr 18, 2012 at 7:07	vote	accept	Jesko Hüttenhain
Apr 17, 2012 at 21:25	comment	added	Jesko Hüttenhain		In fact, I am asking for conditions that I do not have to talk about (semi-)stability. I can very much understand $V/G$ as a set, and now I am asking when it is possible to understand it as $\mathrm{Spec}(A^G)$, where $A$ is the coordinate ring of $V$ and $A^G$ are the functions left invariant by $G$.
Apr 17, 2012 at 18:46	comment	added	Dan Petersen		You're not going to figure this out without rolling up your sleeves and reading a bit of GIT, or an equivalent like Dolgachev's book. For instance you write "the quotient $V/G$" as if it's obvious what this means. For finite $G$ it's obvious, but in general you need to talk about the so-called semi-stable locus for the action and the notion of a "good geometric quotient". If you have digested these things then you will understand Angelo's answer below, too.
Apr 17, 2012 at 18:15	history	edited	Jesko Hüttenhain	CC BY-SA 3.0	added 105 characters in body; added 112 characters in body
Apr 17, 2012 at 18:01	answer	added	Jim Humphreys		timeline score: 6
Apr 17, 2012 at 17:15	comment	added	Misha		See en.wikipedia.org/wiki/Geometric_invariant_theory
Apr 17, 2012 at 16:50	answer	added	Ben McKay		timeline score: 10
Apr 17, 2012 at 16:50	answer	added	Angelo		timeline score: 10
Apr 17, 2012 at 16:44	history	asked	Jesko Hüttenhain	CC BY-SA 3.0