Algebraic group actions on normal varieties
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Abstract:
Let $G$ be a connected algebraic $k$-group acting on a normal $k$-variety, where $k$ is a field. We show that $X$ is covered by open $G$-stable quasi-projective subvarieties; moreover, any such subvariety admits an equivariant embedding into the projectivization of a $G$–linearized vector bundle on an abelian variety, quotient of $G$. This generalizes a classical result of Sumihiro for actions of smooth connected affine algebraic groups.References
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Bibliographic Information
- M. Brion
- Affiliation: Université Grenoble Alpes, Institut Fourier, Grenoble
- MR Author ID: 41725
- Email: michel.brion@univ-grenoble-alpes.fr
- Published electronically: December 1, 2017
- © Copyright 2017 M. Brion
- Journal: Trans. Moscow Math. Soc. 2017, 85-107
- MSC (2010): Primary 14K05, 14L15, 14L30, 20G15
- DOI: https://doi.org/10.1090/mosc/263
- MathSciNet review: 3738079