Geodesic
Equivariant embeddings of commutative linear algebraic groups of corank one
Documenta mathematica, Tome 20 (2015), pp. 1039-1053
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Let K be an algebraically closed field of characteristic zero, Gm​=(K∖0,×) be its multiplicative group, and Ga​=(K,+) be its additive group. Consider a commutative linear algebraic group G=(Gm​)r×Ga​. We study equivariant G-embeddings, i.e. normal G-varieties X containing G as an open orbit. We prove that X is a toric variety and all such actions of G on X correspond to Demazure roots of the fan of X. In these terms, the orbit structure of a G-variety X is described.
DOI : 10.4171/dm/512
Classification : 13N15, 14J50, 14M17, 14M25, 14M27
Mots-clés : toric variety, Cox ring, locally nilpotent derivation, Demazure root 
@article{10_4171_dm_512,
     author = {Ivan Arzhantsev and Polina Kotenkova},
     title = {Equivariant embeddings of commutative linear algebraic groups of corank one},
     journal = {Documenta mathematica},
     pages = {1039--1053},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/512},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/512/}
}
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Ivan Arzhantsev; Polina Kotenkova. Equivariant embeddings of commutative linear algebraic groups of corank one. Documenta mathematica, Tome 20 (2015), pp. 1039-1053. doi: 10.4171/dm/512

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