The set of fixed points of a unipotent group

JOURNAL OF ALGEBRA

卷:322

Article

Jelonek, Zbigniew¹  Lason, Michal^1,2 

[1] Polish Acad Sci, Inst Matemat, PL-31027 Krakow, Poland

[2] Uniwersytet Jagiellonski, Wydzial Matemat & Informat, PL-30348 Krakow, Poland

关键词: Affine variety;    Unipotent algebraic group;    Set of fixed points;   

DOI  :  10.1016/j.jalgebra.2009.06.007

来源: Elsevier

【 摘 要 】

Let K be an algebraically closed field. Let G be a non-trivial connected unipotent group, which acts effectively on an affine variety X. Then every non-empty component R of the set of fixed points of G is a K-uniruled variety, i.e., there exist an affine cylinder W x K and a dominant, generically-finite polynomial mapping phi : W x K -> R. We show also that if an arbitrary infinite algebraic group G acts effectively on K-n and the set of fixed points contains a hypersurface H, then this hypersurface is K-uniruled. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free