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arXiv · 1203.2902

On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev·Ivan Bazhov
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Abstract

Let X be an affine toric variety. The total coordinates on X provide a canonical presentation of X as a quotient of a vector space 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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Ivan Arzhantsev, Ivan Bazhov. 2012-03-13. On orbits of the automorphism group on an affine toric variety. https://doi.org/10.2478/s11533-013-0273-1

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