
Journal of Lie Theory 20 (2010), No. 2, 283293 Copyright Heldermann Verlag 2010 Homogeneous Toric Varieties Ivan V. Arzhantsev Department of Higher Algebra, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory 1, Moscow 119991, Russia arjantse@mccme.ru Sergey A. Gaifullin Department of Higher Algebra, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory 1, Moscow 119991, Russia sgayf@yandex.ru 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 Gmodule structure of V. Keywords: Toric variety, homogeneous space, Cox construction. MSC: 14L30, 14M17, 14M25 [ Fulltextpdf (188 KB)] for subscribers only. 