Algebraic group actions on normal varieties

M. Brion

Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 78 (2017) no. 1, pp. 101-128.

Résumé

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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