Given a fan $\Sigma$ and suppose the corresponding toric variety $X_{\Sigma}$ is invariant under the action of a subgroup of the torus. Does this imply any sort of invariance of the fan? Or, more generally, does the action of the torus on $X_\Sigma$ induce an action of the torus on $\Sigma$?
2025-01-13 05:39:16.1736746756
Torus Action on Fan of Variety
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