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Transactions of the Moscow Mathematical Society

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Algebraic group actions on normal varieties


Author: M. Brion
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2017, 85-107
MSC (2010): Primary 14K05, 14L15, 14L30, 20G15
DOI: https://doi.org/10.1090/mosc/263
Published electronically: December 1, 2017
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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.


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Additional Information

M. Brion
Affiliation: Université Grenoble Alpes, Institut Fourier, Grenoble
Email: michel.brion@univ-grenoble-alpes.fr

DOI: https://doi.org/10.1090/mosc/263
Keywords: Algebraic group actions, linearized vector bundles, theorem of the square, Albanese morphism
Published electronically: December 1, 2017
Article copyright: © Copyright 2017 M.Brion

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