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Статья

Linear bounds for levels of stable rationality

Central European Journal of Mathematics. 2012. Vol. 10. No. 2. P. 466-520.
Bogomolov F. A., Böhning C., Graf von Bothmer H.
Let G be one of the groups SL n(ℂ), Sp 2n(ℂ), SO m(ℂ), O m(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 × ℙ N 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.