Journal of Lie Theory 20 (2010), No. 2, 283--293
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 G-module structure of V.
Keywords: Toric variety, homogeneous space, Cox construction.
MSC: 14L30, 14M17, 14M25
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