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Article

Equivariant Embeddings of Commutative Linear Algebraic Groups of Corank One

Documenta Mathematica. 2015. Vol. 20. P. 1039-1053.

Let K be an algebraically closed field of characteristic zero, G_m be its multiplicative group, and G_a be its additive group. Consider a linear algebraic group G=(G_m)^r\times G_a. We study equivariant G-embeddings, i.e. normal G-varieties X which contains G as an open orbit.  We prove that X is a toric varieties and all such embeddings comes from Demazure roots of the corresponding fan of polyhedral cones.