%0 Journal Article
%T The set of fixed points of a unipotent group
%A Zbigniew Jelonek
%A Micha£¿ Laso¨½
%J Mathematics
%D 2014
%I arXiv
%R 10.1016/j.jalgebra.2009.06.007
%X 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 exists an affine cylinder $W\times K$ and a dominant, generically-finite polynomial mapping $\phi:W\times K\rightarrow R.$ 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.
%U http://arxiv.org/abs/1411.5650v1