Moscow University Mathematics Bulletin

, Volume 74, Issue 5, pp 209–211 | Cite as

Geometrical Description of Orbits of Automorphism Group of Affine Toric Varieties

  • A. A. ShafarevichEmail author
Brief Communications


Let X be an affine toric variety over an algebraically closed field of characteristic zero. Orbits of connected component of identity of automorphism group in terms of dimensions of tangent spaces of the variety X are described. A formula to calculate these dimensions is presented.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Ramanujam, “A Note on Automorphism Group of Algebraic Varieties,” Math. Ann. 156 (1), 25 (1964).MathSciNetCrossRefGoogle Scholar
  2. 2.
    I. V. Arzhantsev, K. G Kuyumzhiyan, and M. G. Zaidenberg, “Flag Varieties, Toric Varieties, and Suspensions: Three Instances of Infinite Transitivity,” Matem. Sbornik 203 (7), 3 (2012) [Sbornik: Math. 203 (7), 923 (2012)].CrossRefGoogle Scholar
  3. 3.
    I. Bazhov, “On Orbits of the Automorphism Group on a Complete Toric Variety,” Beitr. Algebra und Geometrie 54 (2), 471 (2013).MathSciNetCrossRefGoogle Scholar
  4. 4.
    I. Arzhantsev and I. Bazhov, “On Orbits of the Automorphism Group on an Affine Toric Variety,” Open Math. 11 (10), 1713 (2013).MathSciNetCrossRefGoogle Scholar
  5. 5.
    D. Cox, J. Littl, and H. Schenck, Toric Varieties (Amer. Math. Soc, Providence, 2011).Google Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations