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I have a queestion about the proof of Lemma 2.2 from the paper arxiv 1105.3739: Let $G$ be a group acting faithfully on an irreducible affine variety $X=\operatorname{Spec}(A)$ over $k= \Bbb C$. ...

Let $G$ be a connected reductive algebraic group and $X$ be a $G$-variety. Let $Y$ be a $G$-invariant irreducible sub variety of $X$ which has non-trivial intersection with the semi stable locus $X^{...

Let $G$ be an algebraic group over a field $k$, and $\mathbb{P}(V)$ is a projective space. Then Mumford said in his book Geometric Invariant Theory that there's a equivalence between the set of all ...