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Article

On orbits of the automorphism group on an affine toric variety

Central European Journal of Mathematics. 2013. Vol. 11. No. 10. P. 1713-1724.
Arzhantsev I., Bazhov I.

Let X be an affine toric variety. The total coordinates on X provide a canonical presentation !X -> X of X as a quotient of a vector space !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.