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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 𝕜 2 𝕜 2 G G is rational for an arbitrary field 𝕜 of characteristic zero.

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