Doklady Mathematics

, Volume 99, Issue 2, pp 132–136 | Cite as

On the Complexity of Reductive Group Actions over Algebraically Nonclosed Field and Strong Stability of the Actions on Flag Varieties

  • V. S. ZhgoonEmail author
  • F. Knop


We prove new results that generalize Vinberg’s complexity theorem for the action of reductive group on an algebraic variety over an algebraically nonclosed field. We provide new results on strong k-stability for actions on flag varieties are given.



The work of V.S. Zhgoon was supported by the project “Study of Group Algebraic Varieties and Their Relations to Algebra, Geometry, and Number Theory,” project no. 0065-2018-0019.


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Scientific Research Institute for System Analysis, Russian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Friedrich-Alexander Universitat Erlangen-Nurnberg Erlangen and NurembergGermany

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