Timeline for Orbits in the open set given by Rosenlicht's result
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2023 at 18:35 | vote | accept | It'sMe | ||
| Feb 2, 2023 at 11:59 | comment | added | Friedrich Knop | The short answer it "no, not in this generality". The very purpose of GIT is to exhibit open sets $U$ for which membership is "decidable". See the preface of Mumford's book. So you have more chances of an affirmative answer if you stick to open subsets produced by GIT. | |
| Jan 12, 2023 at 17:55 | answer | added | Jason Starr | timeline score: 2 | |
| Jan 11, 2023 at 18:55 | comment | added | Jason Starr | The reference that I know is in Koll'ar's book, "Rational curves on algebraic varieties." I do not have the book with me (I usually do, but not now). So I cannot point to a specific page number, but it is in the section where he discusses quotients by algebraic equivalence relations (such as the equivalence relation of lying in a common orbit for a group action). | |
| Jan 11, 2023 at 18:17 | comment | added | It'sMe | @JasonStarr thanks for your reply. Do you have any references where I can read about such construction? | |
| Jan 11, 2023 at 11:54 | comment | added | Jason Starr | The construction that I know depends on an auxiliary $G$-invariant dense open immersion $i:X\hookrightarrow \overline{X}$. Then the maximal $G$-invariant open subset on which $G$-orbits in $\overline{X}$ are flat is contained in Rosenlicht's open subset. | |
| Jan 11, 2023 at 3:30 | history | asked | It'sMe | CC BY-SA 4.0 |