Rationality of quotients by linear actions of affine groups

作     者：BOGOMOLOV Fedor BHNING Christian GRAF VON BOTHMER Hans-Christian 

作者机构：Department of Mathematics Courant Institute of Mathematical Sciences New York University Mathematisches Institut University of Gottingen 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2011年第54卷第8期

页      面：1521-1532页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the Natural Science Foundation of USA (Grant No. DMS 0701578) supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Gttingen 

主　　题：rationality linear group quotients affine groups 

摘      要：LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).