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.
Key words and phrases:algebraic group actions, linearized vector bundles, theorem of the
square, Albanese morphism.
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