Algebraic group actions on normal varieties

2017/03/28 by Brion, Michel · 1 citation
#14K05 #14L15 #14L30 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.09506

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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