Rationality of the quotient of ${\mathbb{P}}^2$ by finite group of automorphisms over arbitrary field of characteristic zero

Abstract

Let $\mathbb{k}$ be a field of characteristic zero and $G$ be a finite group of automorphisms of projective plane over $\mathbb{k}$. Castelnuovo's criterion implies that the quotient of projective plane by $G$ is rational if the field $\mathbb{k}$ is algebraically closed. In this paper we prove that ${\mathbb{P}}_{\mathbb{k}}^2/G$ is rational for an arbitrary field $\mathbb{k}$ of characteristic zero.

arXiv comment15 pages, 1 figure