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