# Tagged Questions

**7**

votes

**1**answer

369 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

**2**answers

661 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

**1**answer

325 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 ...