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

✍ Scribed by Trepalin, Andrey

• Book ID: 121602338
• Publisher: Walter de Gruyter GmbH
• Year: 2014
• Tongue: English
• Weight: 901 KB
• Volume: 12
• Category: Article
• ISSN: 2391-5455
• DOI: 10.2478/s11533-013-0340-7

✦ Synopsis

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.