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Regular version of the site

Laboratory on Algebraic Transformation Groups

Publications
Article
Automorphisms of algebraic varieties and infinite transitivity

Arzhantsev I.

St Petersburg Mathematical Journal. 2023. Vol. 34. No. 2. P. 143-178.

Article
Euler-symmetric projective toric varieties and additive actions

Shafarevich A.

Indagationes Mathematicae. 2023. Vol. 34. No. 1. P. 42-53.

Article
Root subgroups on affine spherical varieties

Ivan Arzhantsev, Roman Avdeev.

Selecta Mathematica, New Series. 2022. Vol. 28. No. 3.

Article
Tits-type Alternative for Groups Acting on Toric Affine Varieties

Arzhantsev I., Zaidenberg M.

International Mathematics Research Notices. 2022. Vol. 2022. No. 11. P. 8162-8195.

Article
When is the automorphism group of an affine variety nested?

Perepechko A., Regeta A.

Transformation Groups. 2023. Vol. 28. P. 401-412.

Article
Automorphisms of Danielewski varieties

Gayfullin S.

Journal of Algebra. 2021. No. 573. P. 364-392.

The theory of algebraic transformation groups, i.e. actions of algebraic groups on algebraic varieties, is one of the classical areas of algebra and algebraic geometry. It has many interconnections with combinatorics, differential geometry, algebraic group theory, Lie groups, Lie algebras, and representation theory.

One of the main objects of our study is affine algebraic varieties. On the one hand, affine geometry studies local properties of arbitrary algebraic varieties, on the other hand, it gives a geometric interpretation of natural questions in commutative and differential algebra. The combination of algebraic, geometric, representation-theoretical and combinatorial methods allows us to use a wide range of tools in modern mathematics and obtain original results.

The laboratory organizes regularly conferences, schools and seminars in affine algebraic geometry and transformation groups. Within the laboratory, students have an opportunity to work on modern research projects, to publish their results in leading mathematical journals and to take part in international collaborations.

Research area:

  • Automorphism groups of algebraic varieties
  • Varieties with torus actions and graded algebras
  • Additive actions on complete varieties
  • Locally nilpotent derivations
  • Cox rings and their applications
Laboratory staff at Summer school "Visions of algebraic groups", Euler Institute, Saint Petersburg, August 2019
https://www.sites.google.com/view/agmspb2019/events/summer-school