Geodesic
Geometrical description of orbits of automorphism group of affine toric varieties
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 55-58 
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/
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     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},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Ramanujam C., “A note on automorphism group of algebraic varieties”, Math. Ann., 156:1 (1964), 25–33 | DOI | MR | Zbl

[2] Arzhantsev I.V., Zaidenberg M.G., Kuyumzhiyan K.G., “Mnogoobraziya flagov, toricheskie mnogoobraziya i nadstroiki: tri primera beskonechnoi tranzitivnosti”, Matem. sb., 203:7 (2012), 3–30 | DOI | MR | Zbl

[3] Bazhov I., “On orbits of the automorphism group on a complete toric variety”, Beitr. Algebra und Geometrie, 54:2 (2013), 471–481 | DOI | MR | Zbl

[4] Arzhantsev I., Bazhov I., “On orbits of the automorphism group on an affine toric variety”, Open Math., 11:10 (2013), 1713–1724 | DOI | MR | Zbl

[5] Cox D., Little J., Schenck H., Toric Varieties, Amer. Math. Soc., Providence, 2011 | MR | Zbl