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Автоморфизмы двумерных квадрик
Математический сборник. 2026. Т. 217. № 1. С. 29–53.
The maximum possible values of the Jordan constant of the automorphism group of a smooth rational two-dimensional quadric over a field of characteristic zero are found in their dependence on the arithmetic properties of the field.
Semenov A., В кн.: Всемирный конгресс (26–30 июня 2023 г., Москва). Теория систем, алгебраическая биология, искусственный интеллект: математические основы и приложения: Избранные труды.: М.: [б.и.], 2023. С. 390–405.
Added: March 13, 2024
Anton Shafarevich, Anton Trushin, Mathematical Communications 2023 Vol. 28 No. 2 P. 277–291
Let K be an algebraically closed field of characteristic zero. An affine algebraic variety X over K is toral if it is isomorphic to a closed subvariety of a torus K*. We study the group Aut(X) of regular automorpshims of a toral variety X. We prove that if T is a maximal torus in Aut(X), then X is ...
Added: October 19, 2023
Semenov A., Сопрунов С. Ф., Чебышевский сборник 2021 Т. 22 № 1(77) С. 304–327
The article presents results and open problems related to definability spaces (reducts) and sources of this field since the XIX century. Finiteness conditions and constraints are investigated, including the depth of quantifier alternation and the number of arguments. Results related to the description of lattices of definability spaces for numerical and other natural structures are ...
Added: March 11, 2023
Boldyrev I., Gayfullin S., Математические заметки 2021 Т. 110 № 6 С. 837–855
Criteria for the flexibility, rigidity, and almost rigidity of nonnormal affine toric varieties are obtained. For rigid and almost rigid toric varieties, automorphism groups are explicitly calculated. ...
Added: February 6, 2022
Shramov K., Chen Y., / Series arXiv "math". 2021.
We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and p-Jordan property. In particular, we show that the Cremona group of rank 2 over a field of characteristic p>0is p-Jordan, and the birational automorphism group of an arbitrary geometrically irreducible algebraic surface is nilpotently p-Jordan of class at most 2. ...
Added: November 22, 2021
Бухштабер В.М., Тертычный С. И., Функциональный анализ и его приложения 2016 Т. 50 № 3 С. 12–33
Two new linear operators determining automorphisms of the solution space of a special double-confluent Heun equation in the general case are obtained. This equation has two singular points, both of which are irregular. The obtained result is applied to solve the nonlinear equation of the resistively shunted junction model for an overdamped Josephson junction in ...
Added: June 17, 2021
Arzhantsev I., Communications in Algebra 2018 Vol. 46 No. 8 P. 3539–3552
A non-degenerate toric variety X is called S-homogeneous if the subgroup of the automorphism group Aut(X) generated by root subgroups acts on X transitively. We prove that maximal S-homogeneous toric varieties are in bijection with pairs (P,A), where P is an abelian group and A is a finite collection of elements in P such that A generates the group P and for every a∈A the element a is contained in the semigroup generated by A∖{a}. We show that any ...
Added: April 20, 2018
Amerik E., Verbitsky M., Compositio Mathematica 2017 Vol. 153 No. 8 P. 1610–1621
Let M be an irreducible holomorphic symplectic (hyperkähler) manifold. If b 2 (M ) > 5, we construct a deformation M 0 of M which admits a symplectic automorphism of infinite order. This automorphism is hyperbolic, that is, its action on the space of real (1, 1)-classes is hyperbolic. If b 2 (M ) > ...
Added: November 6, 2017
Cheltsov Ivan, Wilson A., Journal of Geometric Analysis 2013 Vol. 23 No. 3 P. 1257–1289
We classify smooth del Pezzo surfaces whose α-invariant of Tian is bigger than 1. ...
Added: November 14, 2013