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On orbits of the automorphism group on an affine toric variety |
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| Authors: | Ivan Arzhantsev Ivan Bazhov |
| Affiliation: | 1273. Department of Higher Algebra, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia 2273. School of Applied Mathematics and Information Science, National Research University Higher School of Economics, Pokrovskiy Boulevard 11, Moscow, 109028, Russia |
| Abstract: | Let X be an affine toric variety. The total coordinates on X provide a canonical presentation $bar X to X$ of X as a quotient of a vector space $bar X$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation. |
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