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Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin — 2014

Open Mathematics

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

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