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

Central European Journal of Mathematics. 2014. Vol. 12. No. 2. P. 229–239.

Andrey S. Trepalin

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

Ключевые слова: rationality, рациональность, Cremona group, Группа Кремоны, Minimal model program, del Pezzo surface, поверхность дель Пеццо, Noether problem, Проблема Нётер, программа минимальных моделей