Abstract:
Let GG be a connected algebraic kk-group acting on a normal kk-variety,
where kk is a field. We show that XX is covered by open GG-stable
quasi-projective subvarieties; moreover, any such subvariety admits an
equivariant embedding into the projectivization of a GG–linearized vector
bundle on an abelian variety, quotient of GG. This generalizes a classical
result of Sumihiro for actions of smooth connected affine algebraic groups.
Key words and phrases:
algebraic group actions, linearized vector bundles, theorem of the
square, Albanese morphism.
Citation:
M. Brion, “Algebraic group actions on normal varieties”, Tr. Mosk. Mat. Obs., 78, no. 1, MCCME, M., 2017, 101–128; Trans. Moscow Math. Soc., 78 (2017), 85–107
\Bibitem{Bri17}
\by M.~Brion
\paper Algebraic group actions on normal varieties
\serial Tr. Mosk. Mat. Obs.
\yr 2017
\vol 78
\issue 1
\pages 101--128
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo594}
\elib{https://elibrary.ru/item.asp?id=37045056}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2017
\vol 78
\pages 85--107
\crossref{https://doi.org/10.1090/mosc/263}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85037663864}
Linking options:
https://www.mathnet.ru/eng/mmo594
https://www.mathnet.ru/eng/mmo/v78/i1/p101
This publication is cited in the following 8 articles:
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Lucy Moser-Jauslin, Ronan Terpereau, “Forms of almost homogeneous varieties over perfect fields”, Annales Henri Lebesgue, 7 (2024), 357
Pascal Fong, Sokratis Zikas, “Connected algebraic subgroups of groups of birational transformations not contained in a maximal one”, Comptes Rendus. Mathématique, 361:G1 (2023), 313
Pascal Fong, “Connected algebraic groups acting on algebraic surfaces”, Annales de l'Institut Fourier, 2023, 1
Eric Primozic, “Motivic cohomology and infinitesimal group schemes”, Ann. K-Th., 7:3 (2022), 441
Bruno Laurent, “Almost Homogeneous Varieties of Albanese Codimension One”, International Mathematics Research Notices, 2022:10 (2022), 7304
Michel Brion, “On models of algebraic group actions”, Proc Math Sci, 132:2 (2022)
J. Schneider, S. Zimmermann, “Algebraic subgroups of the plane Cremona group over a perfect field”, Epijournal Geom. Algebr., 5 (2021)
Citation in format AMSBIB
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