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

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

2011-10-28

arxiv.org/abs/1110.6338v1

Mathematics

Algebraic Geometry

17 pages, 4 figures

Scientific paper

Let $\mathrm{k}$ be a field, $\mathrm{char} \mathrm{k} = 0$ and $G$ be a finite group of authomorphisms of $\mathbb{P}^2_{\mathrm{k}}$. Castelnuovo's Theorem implies that the quotient variety $\mathbb{P}^2_{\mathrm{k}} / G$ is rational if the field $\mathrm{k}$ is algebraically closed. In this paper we prove that the quotient $\mathbb{P}^2_{\mathrm{k}} / G$ is rational for an arbitrary field $\mathrm{k}$ of characteristic zero.

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