Equivariant Embeddings of Algebraic Groups
Equivariant Embeddings of Algebraic Groups
Equivariant Embeddings of Algebraic Groups
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We conclude by describing G-equivariant morphisms between affine G-embeddings in terms<br />
<strong>of</strong> this classification.<br />
In particular, if X 1 → X 2 is a morphism <strong>of</strong> G-embeddings and x i ∈ X i<br />
are base points such that x 1 ↦→ x 2 , then Γ(X 1 , x 1 ) ⊆ Γ(X 2 , x 2 ) and conversely. We characterize<br />
biequivariant affine G-embeddings in terms <strong>of</strong> their cones and construct a canonical “biequivariant<br />
resolution” X G → X <strong>of</strong> any given affine G-embedding X, where X G is a (G × G)-equivariant affine<br />
G-embedding satisfying a universal property.<br />
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