Homogeneous toric varieties
Ivan V. Arzhantsev, Sergey A. Gaifullin

TL;DR
This paper characterizes toric varieties with transitive semisimple group actions, showing they are related to products of affine and projective spaces, using Cox realization and G-module analysis.
Contribution
It provides a classification of toric varieties admitting transitive semisimple group actions, linking them to specific product structures.
Findings
Toric varieties with transitive G-actions are between products of punctured affine spaces and projective spaces.
The Cox realization and G-module structure are key tools in the classification.
The paper offers a structural description of such toric varieties.
Abstract
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics
