2009/07/05 by Zbigniew Jelonek, Michał Lasoń
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Computer science #Fixed point #Geometric and Algebraic Topology #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Physics #Programming language #Pure mathematics #Set (abstract data type) #Unipotent #math.AG #math.GR #msc:14L17
paper · pdf · doi:10.1016/j.jalgebra.2009.06.007
published as Journal of Algebra 322 (2009), no. 6, 2180-2185 · final version, 6 pages
openalex publication_date 2009/07/05 · arxiv created 2014/11/20 · arxiv updated 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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× K and a dominant, generically-finite polynomial mapping ϕ:W× K→ R. We show also that if an arbitrary infinite algebraic group G acts effectively on Kn and the set of fixed points contains a hypersurface H, then this hypersurface is K-uniruled.