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Regular version of the site

Laboratory on Algebraic Transformation Groups

Publications
Article
Lie algebras of vertical derivations on semiaffine varieties with torus actions

Arzhantsev I., Liendo A., Stasyuk T.

Journal of Pure and Applied Algebra. 2021. Vol. 225. No. 2. P. 106499.

Article
Commutative algebraic monoid structures on affine surfaces

Dzhunusov S., Zaitseva Y.

Forum Mathematicum. 2021. Vol. 33. No. 1. P. 177-191.

Article
Automorphisms of Danielewski varieties

Gayfullin S.

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

Article
Commutative algebraic monoid structures on affine spaces

Arzhantsev I., Bragin S., Zaitseva Y.

Communications in Contemporary Mathematics. 2020. Vol. 22. No. 8. P. 1950064: 1.

Article
Infinite transitivity, finite generation, and Demazure roots

Arzhantsev I., Kuyumzhiyan K., Zaidenberg M.

Advances in Mathematics. 2019. Vol. 351. P. 1-32.

Article
Flexibility of normal affine horospherical varieties

Gayfullin S., Shafarevich Anton.

Proceedings of the American Mathematical Society. 2019. Vol. 147. P. 3317-3330.

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
At Summer School "Visions of Algebraic Groups", Euler Institute, Saint Petersburg, August 2019