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On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev; Ivan Bazhov — 2013

Open Mathematics

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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