Geodesic
Equivariant embeddings of commutative linear algebraic groups of corank one
Documenta mathematica, Tome 20 (2015), pp. 1039-1053.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $\KK$ be an algebraically closed field of characteristic zero, $\GG_m=(\KK\setminus{0},\times)$ be its multiplicative group, and $\GG_a=(\KK,+)$ be its additive group. Consider a commutative linear algebraic group $\GG=(\GG_m)^r\times\GG_a$. 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.
Classification : 14M17, 14M25, 14M27, 13N15, 14J50
Keywords: toric variety, Cox ring, locally nilpotent derivation, Demazure root 
@article{DOCMA_2015__20__a12,
     author = {Arzhantsev, Ivan and Kotenkova, Polina},
     title = {Equivariant embeddings of commutative linear algebraic groups of corank one},
     journal = {Documenta mathematica},
     pages = {1039--1053},
     publisher = {mathdoc},
     volume = {20},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a12/}
}
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Arzhantsev, Ivan; Kotenkova, Polina. Equivariant embeddings of commutative linear algebraic groups of corank one. Documenta mathematica, Tome 20 (2015), pp. 1039-1053. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a12/