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2014 | 12 | 2 | 229-239
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Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

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Let $$\Bbbk$$ be a field of characteristic zero and G be a finite group of automorphisms of projective plane over $$\Bbbk$$. Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field $$\Bbbk$$ is algebraically closed. In this paper we prove that $${{\mathbb{P}_\Bbbk ^2 } \mathord{\left/ {\vphantom {{\mathbb{P}_\Bbbk ^2 } G}} \right. \kern-\nulldelimiterspace} G}$$ is rational for an arbitrary field $$\Bbbk$$ of characteristic zero.
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0340-7
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