Suppose $X$ is a toric variety with fan $\Sigma$, and the lattice of its torus is $N$. Suppose there is a representation of finite group $G$, \begin{equation} \phi:G \rightarrow \text{GL}(N \otimes_{\mathbb{Z}} \mathbb{R}) \end{equation} which maps the lattice points of $N$ to lattice points of $N$, and maps the cones of $\Sigma$ to the cones of $\Sigma$.
Question: is the quotient variety $X/G$ (which exists from GIT) still a toric variety?

I guess the answer is yes? Are there references about how to construct the fan of $X/G$?

Edit: I have asked this question on MO.




You must log in to answer this question.

Browse other questions tagged .