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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 12, Issue 2

Issues

Volume 13 (2015)

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

Andrey Trepalin
  • Department of Algebra, Faculty of Mathematics, MSU, Vorobyevy Gory 1, Moscow, 117234, Russia
  • Laboratory of Algebraic Geometry, GU-HSE, Vavilova Str. 7, Moscow, 117312, Russia
  • Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, Moscow, 119002, Russia
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Published Online: 2013-11-21 | DOI: https://doi.org/10.2478/s11533-013-0340-7

Abstract

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.

MSC: 14E07; 14E08; 14L30; 14M20; 13A50

Keywords: Noether problem; Rationality; del Pezzo surfaces; Minimal Model Program; Cremona group

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About the article

Published Online: 2013-11-21

Published in Print: 2014-02-01


Citation Information: Open Mathematics, Volume 12, Issue 2, Pages 229–239, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0340-7.

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