A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety as a quotient space of an open subset of a vector space V by a quasitorus action and on investigation of the G-module structure of V.
1
Department of Higher Algebra, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory 1, Moscow 119991, Russia
Ivan V. Arzhantsev; Sergey A. Gaifullin. Homogeneous Toric Varieties. Journal of Lie Theory, Tome 20 (2010) no. 2, pp. 283-293. http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a2/
@article{JOLT_2010_20_2_a2,
author = {Ivan V. Arzhantsev and Sergey A. Gaifullin},
title = {Homogeneous {Toric} {Varieties}},
journal = {Journal of Lie Theory},
pages = {283--293},
year = {2010},
volume = {20},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a2/}
}
TY - JOUR
AU - Ivan V. Arzhantsev
AU - Sergey A. Gaifullin
TI - Homogeneous Toric Varieties
JO - Journal of Lie Theory
PY - 2010
SP - 283
EP - 293
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a2/
ID - JOLT_2010_20_2_a2
ER -
%0 Journal Article
%A Ivan V. Arzhantsev
%A Sergey A. Gaifullin
%T Homogeneous Toric Varieties
%J Journal of Lie Theory
%D 2010
%P 283-293
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a2/
%F JOLT_2010_20_2_a2
