Ivan Arzhantsev, Polina Kotenkova

摘要

Let $KK$ be an algebraically closed field of characteristic zero, $GG_m=(KKsetminus{0},imes)$ be its multiplicative group, and $GG_a=(KK,+)$ be its additive group. Consider a commutative linear algebraic group $GG=(GG_m)^rimesGG_a$. We study equivariant $GG$-embeddings, i.e. normal $GG$-varieties $X$ containing $GG$ as an open orbit. We prove that $X$ is a toric variety and all such actions of $GG$ on $X$ correspond to Demazure roots of the fan of $X$. In these terms, the orbit structure of a $GG$-variety $X$ is described.