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arXiv · 1411.5650

The set of fixed points of a unipotent group

Zbigniew Jelonek·Michał Lasoń
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Abstract

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.

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Zbigniew Jelonek, Michał Lasoń. 2014-11-20. The set of fixed points of a unipotent group. https://doi.org/10.1016/j.jalgebra.2009.06.007

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