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

• Autorzy: Andrey Trepalin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 14E08: Rationality questions
• 14E07: Birational automorphisms, Cremona group and generalizations
• 13A50: Actions of groups on commutative rings; invariant theory
• 14M20: Rational and unirational varieties
• 14L30: Group actions on varieties or schemes (quotients)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 229-239

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Andrey Trepalin

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0340-7