Rationality problem of three-dimensional purely monomial group actions: the last case
Rationality problem of three-dimensional purely monomial group actions: the last case
A $k$-automorphism $\sigma$ of the rational function field $k(x_1,\dots ,x_n)$ is called purely monomial if $\sigma$ sends every variable $x_i$ to a monic Laurent monomial in the variables $x_1,\dots ,x_n$. Let $G$ be a finite subgroup of purely monomial $k$-automorphisms of $k(x_1,\dots ,x_n)$. The rationality problem of the $G$-action is …