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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 $ℙ_{𝕜}^{2} / G$ is rational for an arbitrary field $𝕜$ of characteristic zero.

Rationally connected varieties over local fields.

Kollár, János (1999)

Annals of Mathematics. Second Series

Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II

Fabrizio Catanese, Frédéric Mangolte (2009)

Annales scientifiques de l'École Normale Supérieure

Let $W \to X$ be a real smooth projective 3-fold fibred by rational curves such that $W (ℝ)$ is orientable. J. Kollár proved that a connected component $N$ of $W (ℝ)$ is essentially either Seifert fibred or a connected sum of lens spaces. Answering three questions of Kollár, we give sharp estimates on the number and the multiplicities of the Seifert fibres (resp. the number and the torsions of the lens spaces) when $X$ is a geometrically rational surface. When $N$ is Seifert fibred over a base orbifold $F$ , our result generalizes...

Reduction of the proof of the non-rationality of a non-singular cubic threefold to a result of mumford

J. P. Murre (1973)

Compositio Mathematica

Relations between moduli spaces of stable bundles over ...2 and rationality.

Wei-Ping Li (1997)

Journal für die reine und angewandte Mathematik

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