English

Equivariant embeddings of commutative linear algebraic groups of corank one

Algebraic Geometry 2015-10-21 v1

Abstract

Let K be an algebraically closed field of characteristic zero, G_m=(K\{0},*) be its multiplicative group, and G_a=(K,+) be its additive group. Consider a commutative linear algebraic group G=G_m^r\times G_a. 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.

Keywords

Cite

@article{arxiv.1501.03270,
  title  = {Equivariant embeddings of commutative linear algebraic groups of corank one},
  author = {Ivan Arzhantsev and Polina Kotenkova},
  journal= {arXiv preprint arXiv:1501.03270},
  year   = {2015}
}

Comments

12 pages