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Classification of affine homogeneous spaces of complexity one
Sbornik Mathematics. 2004. Vol. 195. No. 6. P. 765–782.
Arzhantsev I., Chuvashova O. V.
The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. Affine homogeneous spaces G/H of complexity 1 are classified in this paper. These results are the natural continuation of the earlier classification of spherical affine homogeneous spaces, that is, spaces of complexity 0.
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
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Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Arzhantsev I., Shakhmatov K., Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 2026 Vol. 120 Article 55
We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine factorial 3-fold that is not a homogeneous space of an algebraic group. ...
Added: March 24, 2026
Popov V., Успехи математических наук 2025 Т. 80 № 3(483) С. 189–190
It is proved that for any positive integers d and c, the set of isomorphism classes of all d-dimensional reductive algebraic groups with exactly c connected components is finite. As a corollary, the set of isomorphism classes of all d-dimensional compact real Lie groups with exactly c connected components is proved to be finite. To ...
Added: December 16, 2025
Arzhantsev I., Izvestiya. Mathematics 2009 Vol. 73 No. 3 P. 437–453
We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit has codimension at least 2. We establish a criterion for the existence of such an embedding, prove that the set of isomorphism classes of such embeddings is finite, and give a construction of the embeddings in terms of ...
Added: June 13, 2025
Arzhantsev I., Sbornik Mathematics 2001 Vol. 192 No. 8 P. 1133–1138
Let G be a reductive algebraic group and let H be a reductive subgroup of G. The modality of a G-variety X is the largest number of the parameters in a continuous family of G-orbits in X. A precise formula for the maximum value of the modality over all affine embeddings of the homogeneous space ...
Added: June 13, 2025
Arzhantsev I., Sbornik Mathematics 1999 Vol. 190 No. 7 P. 937–954
The language of filtrations and contractions is used to describe the class of G-varieties obtained as the total spaces of the construction of contraction applied to affine spherical varieties, which is well-known in invariant theory.
These varieties are local models for arbitrary affine G-varieties of complexity 1 with a one-dimensional categorical quotient. As examples, reductive algebraic semigroups ...
Added: June 13, 2025
Arzhantsev I., Izvestiya. Mathematics 1997 Vol. 61 No. 4 P. 685–698
This paper is devoted to the actions of the group SL(2) with two-dimensional generic orbit on normal three-dimensional affine algebraic varieties. We obtain a complete classi cation of such actions whenever the stabilizer of general position
is the subgroup of monomial matrices. We also prove some results for arbitrary actions of complexity one of reductive groups. ...
Added: June 13, 2025
Arzhantsev I., Sbornik Mathematics 1997 Vol. 188 No. 5 P. 639–655
Actions of reductive groups on normal algebraic varieties with one-parameter families of spherical orbits of maximal dimension are studied under the assumption that the categorical quotient for the action is one-dimensional. As an application, the classification of the actions of the group SL(2) on three-dimensional normal affine varieties is completed. The ground field K is assumed to be algebraically closed and of characteristic zero. ...
Added: June 13, 2025
Arzhantsev I., Functional Analysis and Its Applications 1997 Vol. 31 No. 4 P. 278–280
Let a connected reductive group G act on a normal affine variety X with the generic stabilizer H, let the complexity of this action be one, and let the categorial quotient X//G be one-dimensional. Then the closure of any G-orbit in X is normal. ...
Added: June 13, 2025
Gorchakov V., Journal of the Mathematical Society of Japan 2025
Added: May 22, 2025
Arzhantsev I., Zaitseva Y., Research in Mathematical Sciences 2024 Vol. 11 No. 2 Article 27
An algebraic variety X is called a homogeneous variety if the automorphism group Aut(X) acts on X transitively, and a homogeneous space if there exists a transitive action of an algebraic group on X. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we ...
Added: March 23, 2024
Ignatev Mikhail, Penkov I., Transformation Groups 2022
We compute the group of automorphisms of an arbitrary ind-variety of (possibly
isotropic) generalized flags. Such an ind-variety is a homogeneous ind-space for
one of the ind-groups SL(∞), O(∞) or Sp(∞). We show that the respective automorphism groups are much larger than SL(∞), O(∞) or Sp(∞), and present the
answer in terms of Mackey groups. The latter are ...
Added: October 8, 2023
Arzhantsev I., Indagationes Mathematicae 2023 Vol. 34 No. 4 P. 812–819
We prove that every non-degenerate toric variety, every homogeneous space of a connected linear algebraic group without non-constant invertible regular functions, and every variety covered by affine spaces admit a surjective morphism from an affine space. ...
Added: May 24, 2023
Ivan V. Arzhantsev, Yulia I. Zaitseva, Kirill V. Shakhmatov, Proceedings of the Steklov Institute of Mathematics 2022 Vol. 318 No. 1 P. 13–25
Let X be an algebraic variety such that the group Aut(X) acts on X transitively. We define the transitivity degree of X as the maximum number m such that the action of Aut(X) on X is m-transitive. If the action of Aut(X) is m-transitive for all m, the transitivity degree is infinite. We compute the transitivity degree for all quasi-affine toric varieties and for many homogeneous spaces of algebraic groups. We also discuss a conjecture and ...
Added: November 5, 2022
Arzhantsev I., Zaitseva Y., Shakhmatov K., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 318 С. 17–30
Let X be an algebraic variety such that the group Aut(X) acts on X transitively. We define the transitivity degree of X as a maximal number m such that the action of Aut(X) on X is m-transitive. If the action of Aut(X) is m-transitive for all m, the transitivity degree is infinite. We compute the transitivity degree for all quasi-affine toric varieties and for many homogeneous spaces of algebraic groups. Also we discuss a ...
Added: November 4, 2022