Linear bounds for levels of stable rationality

Fedor Bogomolov; Christian Böhning; Hans-Christian Graf von Bothmer

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 466-520
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Fedor Bogomolov, Christian Böhning, and Hans-Christian Graf von Bothmer. "Linear bounds for levels of stable rationality." Open Mathematics 10.2 (2012): 466-520. <http://eudml.org/doc/269127>.

@article{FedorBogomolov2012,
abstract = {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.},
author = {Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer},
journal = {Open Mathematics},
keywords = {Rationality; Stable rationality; Linear group quotients; rationality; stable rationality; linear group quotients},
language = {eng},
number = {2},
pages = {466-520},
title = {Linear bounds for levels of stable rationality},
url = {http://eudml.org/doc/269127},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Fedor Bogomolov
AU - Christian Böhning
AU - Hans-Christian Graf von Bothmer
TI - Linear bounds for levels of stable rationality
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 466
EP - 520
AB - 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.
LA - eng
KW - Rationality; Stable rationality; Linear group quotients; rationality; stable rationality; linear group quotients
UR - http://eudml.org/doc/269127
ER -

References

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