All Questions

Let $G$ be a connected complex reductive group. Suppose $G$ acts on a smooth complex affine variety $X$. Assume the stabiliser $G_x$ of every point $x\in X$ is finite. Is it true that $X/\!/G$ is an ...

Let $G$ be a connected complex reductive group with Lie algebra $\mathfrak{g}$. One knows a lot about the GIT quotient $\mathfrak{g}/\!/G$: the invariant ring is a free polynomial algebra on $\mathrm{...

I saw the question When is an almost geometric quotient flat? which said "The quotient $\pi$ is flat if and only if $\pi$ is equidimensional and $X$ is smooth". I am curious is there an ...

Let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic 0 (a reduced separated scheme of finite type over $k$). Let $G$ be a connected linear algebraic group over $k$ (...

All varieties here are over $\Bbb C$. Let $G$ be a reductive algebraic group acting algebraically on affine $n$-space $\Bbb A^n$. Let $R$ be the coordinate ring of $\Bbb A^n$. Assume that the natural ...