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Linear bounds for levels of stable rationality

100%

Bogomolov F., Böhning C., Graf von Bothmer H.-C.

Open Mathematics

2012

tom 10

nr 2

466-520

Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.

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

84%

Trepalin A.

Open Mathematics

2014

tom 12

nr 2

229-239

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.

Ograniczanie wyników

2 Open Mathematics

1 Bogomolov F.

1 Böhning C.

1 Graf von Bothmer H.-C.

1 Trepalin A.

1 2014

1 2012

Wyniki wyszukiwania

Linear bounds for levels of stable rationality

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