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Flexibility of normal affine horospherical varieties
Proceedings of the American Mathematical Society. 2019. Vol. 147. P. 3317-3330.
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only con- stant invertible functions and a locally transitive action of a reductive group is proved. Also we show that a normal affine complexity-zero horospherical variety with only constant invertible functions is flexible.
Gayfullin S., Шафаревич А. А., / Cornell University. Series arXiv "math". 2018. No. arXiv:1805.05024.
Added: September 1, 2018
Gayfullin S., Journal of Algebra 2021 No. 573 P. 364-392
In 2007, Dubouloz introduced Danielewski varieties. Such varieties generalize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to Makar-Limanov. ...
Added: February 6, 2021
Shafarevich A., Математический сборник 2017 Т. 208 № 2 С. 285-310
Let k be an algebraically closed field of characteristic zero and Ga = (k, +) the additive group of k. An algebraic variety X is said to be flexible if the tangent space at every regular point of X is generated by the tangent vectors to orbits of various regular actions of Ga. In 1972, ...
Added: December 5, 2018
Gayfullin S., / Cornell University. Series arXiv "math". 2018.
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also we show that a normal affine complexity-zero horospherical variety is flexible. ...
Added: December 6, 2018
Gayfullin S., / Cornell University. Series arXiv "math". 2018. No. arXiv:1709.09237.
In 2007, Dubouloz introduced Danielewski varieties. Such varieties general- ize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to Makar-Limanov. ...
Added: September 1, 2018
Shafarevich A., Proceedings of the American Mathematical Society 2019 Vol. 147 No. 8 P. 3317-3330
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also we show that a normal affine complexity-zero horospherical variety with only constant invertible functions is flexible. ...
Added: September 10, 2019
Arzhantsev I., Gayfullin S., Mathematische Nachrichten 2017 Vol. 290 No. 5-6 P. 662-671
An irreducible algebraic variety X is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group of a rigid affine variety contains a unique maximal torus . If the grading on the algebra of regular functions defined by the action of is pointed, the group is a finite extension of . As an application, ...
Added: February 19, 2017
Gayfullin S., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 318 С. 43-50
In 2013 Bazhov proved a criterion for two points on a complete toric variety to lie in the same orbit of the neutral component of the automorphism group. This criterion is formulated in terms of the divisor class group. The same year Arzhantsev and Bazhov obtained a similar criterion for affine toric varieties. We prove ...
Added: December 12, 2022
Gayfullin S., Zaitseva Y., Journal of Algebra and its Applications 2019 Vol. 18 No. 10 P. 1950196-1-1950196-14
We provide an explicit description of homogeneous locally nilpotent derivations of the algebra of regular functions on affine trinomial hypersurfaces. As an application, we describe the set of roots of trinomial algebras. ...
Added: September 10, 2019
Vladimir L. Popov, Documenta Mathematica 2015 Vol. Extra Volume: Merkurjev's Sixtieth Birthday P. 513-528
A “rational” version of the strengthened form of the Commuting Derivation Conjecture, in which the assumption of commutativity
is dropped, is proved. A systematic method of constructing in any dimension greater than 3 the examples answering in the negative a question by M. El Kahoui is developed. ...
Added: September 25, 2015
Gayfullin S., Chunaev D., Фундаментальная и прикладная математика 2023 Т. 25
In this work we obtain sufficient conditions for a variety with a torus action of complexity one to have finite number of automorphism group orbits. ...
Added: December 2, 2023
Zaitseva Y., Математические заметки 2019 Т. 105 № 6 С. 824-838
В работе получено описание однородных локально нильпотентных дифференцирований алгебры регулярных функций некоторого класса триномиальных гиперповерхностей. Данный класс включает в себя все нефакториальные триномиальные гиперповерхности. ...
Added: September 19, 2019
Arzhantsev I., Bragin S., Zaitseva Y., Communications in Contemporary Mathematics 2020 Vol. 22 No. 8 P. 1950064: 1
We study commutative associative polynomial operations A^n×A^n→A^n with unit on the affine space A^n over an algebraically closed field of characteristic zero. A classification of such operations is obtained up to dimension 3. Several series of operations are constructed in arbitrary dimension. Also we explore a connection between commutative algebraic monoids on affine spaces and additive actions on toric ...
Added: September 19, 2019
Arzhantsev I., Алгебра и анализ 2022 Т. 34 № 2 С. 1-55
В работе дан обзор результатов последних лет о кратной транзитивности действий групп автоморфизмов аффинных алгебраических многообразий. Рассматривается свойство бесконечной транзитивности действия группы специальных автоморфизмов и эквивалентное ему свойство гибкости многообразия. Данные свойства имеют важные алгебраические и геометрические следствия, и при этом они выполнены для широких классов многообразий. Отдельно изучаются случаи, когда бесконечная транзитивность имеет место ...
Added: March 14, 2022
Bilich B., / Cornell University. Series math "arxiv.org". 2021. No. 2106.04884.
In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional algebraic monoids are toric. We also show how to find all monoid structures on a normal toric surface. Every such structure is induced by ...
Added: June 13, 2021
Arzhantsev I., Bazhov I., Central European Journal of Mathematics 2013 Vol. 11 No. 10 P. 1713-1724
Let X be an affine toric variety. The total coordinates on X provide a canonical presentation !X -> X of X as a quotient of a vector space !X by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the ...
Added: November 13, 2013
Arzhantsev I., Ricerche di Matematica 2024 Vol. 73 No. 2 P. 715-724
We show that an effective action of the one-dimensional torus G_m on a normal affine algebraic variety X can be extended to an effective action of a semi-direct product G_m⋌G_a with the same general orbit closures if and only if there is a divisor D on X that consists of G_m-fixed points. This result is applied to the study of orbits of the automorphism group Aut(X) on X. ...
Added: August 16, 2021
Arzhantsev I., St Petersburg Mathematical Journal 2023 Vol. 34 No. 2 P. 143-178
We survey recent results on multiple transitivity for automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the corresponding affine variety. These properties have important algebraic and geometric consequences. At the same time they are fulfilled for wide classes of ...
Added: March 30, 2023
Perepechko A., Forum Mathematicum 2021 Vol. 33 No. 2 P. 339-348
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on ...
Added: January 15, 2021
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020