Geodesic
Geometrical description of orbits of automorphism group of affine toric varieties
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 55-58

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Let $X$ be an affine toric variety over an algebraically closed field of characteristic zero. In this paper we describe orbits of connected component of identity of automorphism group in terms of dimensions of tangent spaces of the variety $X$. We also present a formula to calculate these dimensions. 
@article{VMUMM_2019_5_a10,
     author = {A. A. Shafarevich},
     title = {Geometrical description of orbits of automorphism group of affine toric varieties},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {55--58},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a10/}
}
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A. A. Shafarevich. Geometrical description of orbits of automorphism group of affine toric varieties. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 55-58. http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a10/