TY - JOUR
T1 - Linear bounds for levels of stable rationality
AU - Bogomolov, Fedor
AU - Böhning, Christian
AU - von Bothmer, Hans Christian Graf
N1 - 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 Göttingen. 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 Göttingen.
PY - 2012/4
Y1 - 2012/4
N2 - 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.
AB - 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.
KW - Linear group quotients
KW - Rationality
KW - Stable rationality
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U2 - 10.2478/s11533-011-0097-9
DO - 10.2478/s11533-011-0097-9
M3 - Article
AN - SCOPUS:84856017333
SN - 1895-1074
VL - 10
SP - 466
EP - 520
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 2
ER -