@article{cfa171f98431470da8eafd4f6fef2309,
title = "Linear bounds for levels of stable rationality",
abstract = "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.",
keywords = "Linear group quotients, Rationality, Stable rationality",
author = "Fedor Bogomolov and Christian B{\"o}hning and {von Bothmer}, {Hans Christian Graf}",
note = "Funding Information: During the work the first author was partially supported by NSF grant DMS-1001662 and by AG Laboratory GU-HSE grant RF government ag. 11 11.G34.31.0023. The second and third authors were supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of G{\"o}ttingen. The second author wants to thank the University of Vienna for hospitality during a stay in the summer of 2010 where this work began to take shape. Funding Information: Second and third author supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of G{\"o}ttingen.",
year = "2012",
month = apr,
doi = "10.2478/s11533-011-0097-9",
language = "English (US)",
volume = "10",
pages = "466--520",
journal = "Open Mathematics",
issn = "1895-1074",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "2",
}