Timeline for Equivariant form of Nagata's compactification theorem?
Current License: CC BY-SA 3.0
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| Nov 25, 2015 at 13:50 | comment | added | nfdc23 | Yes, this can be done in a simple way that doesn't require any use of quotients (or freeness hypotheses on the action), by a technique which comes up (in a slightly different way) in the proof of the compactification theorem for algebraic spaces (if you read it). Let $j:X \hookrightarrow Y$ be an initial choice of compactification. Define $f:X \rightarrow Y^G := \prod_{g \in G} Y$ by $x \mapsto (j(g^{-1}x))$. Then $f$ is an immersion (exercise) and $G$-equivariant where $G$ acts on $Y^G$ via $g_0.(x_g) = (x_{g_0^{-1}g})$. Let $\overline{X}$ be the schematic image of $X$. | |
| Nov 25, 2015 at 13:30 | history | asked | Dominik | CC BY-SA 3.0 |