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LSpice
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smoothness Smoothness of Orbitorbit of group scheme

Let $G$ be a smooth affine group scheme over a base $S$. $G$ acts on a scheme $X$ over $S$. Let $x$ be aan $S$-point in $X$. Then we can have aan orbit map $G\to X$. I wonder when the image (set-theoretically) of this map is locally closed, and the induced scheme structure (the minimal one) on the orbit is smooth over $S$. Thanks.

smoothness of Orbit of group scheme

Let $G$ be a smooth affine group scheme over a base $S$. $G$ acts on a scheme $X$ over $S$. Let $x$ be a $S$-point in $X$. Then we can have a orbit map $G\to X$. I wonder when the image (set-theoretically) of this map is locally closed, and the induced scheme structure (the minimal one) on the orbit is smooth over $S$. Thanks.

Smoothness of orbit of group scheme

Let $G$ be a smooth affine group scheme over a base $S$. $G$ acts on a scheme $X$ over $S$. Let $x$ be an $S$-point in $X$. Then we have an orbit map $G\to X$. I wonder when the image (set-theoretically) of this map is locally closed, and the induced scheme structure (the minimal one) on the orbit is smooth over $S$.

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JJH
JJH
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smoothness of Orbit of group scheme

Let $G$ be a smooth affine group scheme over a base $S$. $G$ acts on a scheme $X$ over $S$. Let $x$ be a $S$-point in $X$. Then we can have a orbit map $G\to X$. I wonder when the image (set-theoretically) of this map is locally closed, and the induced scheme structure (the minimal one) on the orbit is smooth over $S$. Thanks.