Timeline for Quotient $(V -S)/G$ is a quasi-projective variety for every closed $S \subset V$ with free $G$-action
Current License: CC BY-SA 4.0
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| Nov 2, 2021 at 4:44 | comment | added | abx | You just need $S$ to be stable under $G$. The fact that the action on $V-S$ is free is crucial for the rest of the paper, so I think Totaro just kept it in the Remark. The "concrete GIT result" is the fact that $V/G$ is a geometric quotient and an affine variety. | |
| Nov 1, 2021 at 23:21 | comment | added | user267839 | @abx: Is the premise that the $G$-action on $V-S$ is free crucial for this statement, or can it be weakened here? It seems to be quite strong, and in GIT I haven't found a result which uses this free action premise in essential way to garantee that $(V-S)/G$ carry open variety in $V/G$. The question remains, to which concrete GIT result exactly is Totaro referring to? | |
| Nov 1, 2021 at 5:32 | review | Close votes | |||
| Nov 18, 2021 at 21:15 | |||||
| Nov 1, 2021 at 5:15 | comment | added | abx | $(V-S)/G$ is an open subvariety of the affine variety $V/G$. | |
| Nov 1, 2021 at 4:09 | history | asked | user267839 | CC BY-SA 4.0 |