Linear bounds for levels of stable rationality

TL;DR

This paper establishes linear bounds on the levels of stable rationality for quotients of generically free representations of classical groups, improving previous bounds and analyzing their growth relative to the group's rank.

Contribution

It provides improved, linear bounds for the levels of stable rationality of V/G for classical groups, advancing understanding of their rationality properties.

Findings

Linear growth of stable rationality levels with group rank for classical groups

Enhanced bounds for the levels of stable rationality

Analysis of rationality properties of quotients V/G

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 x 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 one of the classical groups.