Algebraic group actions on normal varieties - Archive ouverte HAL
Article Dans Une Revue Transactions of the Moscow Mathematical Society Année : 2017

Algebraic group actions on normal varieties

Michel Brion

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.

Dates et versions

hal-02020800 , version 1 (15-02-2019)

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Citer

Michel Brion. Algebraic group actions on normal varieties. Transactions of the Moscow Mathematical Society, 2017, 78, pp.85-107. ⟨10.1090/mosc/263⟩. ⟨hal-02020800⟩
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