7
votes
1answer
349 views

Why people usually consider reductive groups in GIT?

Where do people essentially use the reductive groups in the theory of GIT? Or how does reductive groups simplify the constructions in GIT? I found that the property of completely reducible of ...
11
votes
2answers
638 views

Is an affine “G-variety” with reductive stabilizers a toric variety?

Let $X=Spec(A)$ be a reduced normal affine scheme over an algebraically closed field $k$ of characteristic $0$, with an action of a connected reductive group $G$. Suppose $x\in X$ is a ...
5
votes
1answer
321 views

If Spec(A) has a G-fixed point and a dense G-orbit, is Spec(A) a cone?

[Edited to include a dense orbit] Let $X=Spec(A)$ be a normal affine scheme over an algebraically closed field $k$, with an action of a linearly reductive group $G$. Suppose $x\in X$ is a ...