?
Ga-actions on affine cones
Transformation Groups. 2013. Vol. 18. No. 4. P. 1137-1153.
We give a criterion of existence of a unipotent group action on the affine cone over a projective variety or, more generally, on the affine quasicone over a variety which is projective over another affine variety.
Kishimoto T., Yuri Prokhorov, Zaidenberg M., Algebraic Geometry 2014 Vol. 1 No. 1 P. 46-56
In a previous paper we established that for any del Pezzo surface Y of degree at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear system admits an effective Ga-action. In particular, the group Aut(X) is infinite dimensional. In contrast, we show in this note that for a del Pezzo surface ...
Added: October 10, 2013
Kishimoto T., Yuri Prokhorov, Zaidenberg M., Osaka Journal of Mathematics 2014 Vol. 51 No. 4 P. 1093-1113
We address the following question: When an affine cone over a smooth Fano threefold admits an effective action of the additive group? In this paper we deal with Fano threefolds of index 1 and Picard number 1. Our approach is based on a geometric criterion from our previous paper, which relates the existence of an ...
Added: October 10, 2013
Kishimoto T., Prokhorov Y., Zaidenberg M., , in : CRM Proceedings & Lecture Notes. Vol. 54: Affine Algebraic Geometry: The Russell Festschrift.: Providence : American Mathematical Society, 2011. P. 123-163.
In this article, the authors study the action of the additive group C on affine cones over projective varieties. They show that such actions always exist for the cones over del Pezzo surfaces of degree d≥4 which are canonically embedded, and give relations between the actions and existence of polar cylinders. The case of del ...
Added: October 14, 2013
Perepechko A., Функциональный анализ и его приложения 2013 Т. 47 № 4 С. 45-52
We prove that the action of the special automorphism group on affine cones over del Pezzo surfaces of degree 4 and 5 is infinitely transitive. ...
Added: September 26, 2019
Prokhorov Y., Springer Proceedings in Mathematics & Statistics 2014 Vol. 79 P. 215-229
We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds. ...
Added: January 24, 2014
Yuri Prokhorov, / Cornell University. Series math "arxiv.org". 2011.
We prove that for a Q-Gorenstein degeneration $X$ of del Pezzo surfaces, the number of non-Du Val singularities is at most $\rho(X)+2$. Degenerations with $\rho(X)+2$ and $\rho(X)+1$ non-Du Val points are investigated. ...
Added: October 11, 2013
Prokhorov Y., Annales de l'Institut Fourier 2015 No. 65 P. 1-16
We prove that for a Q-Gorenstein degeneration $X$ of del Pezzo surfaces, the number of non-Du Val singularities is at most $\rho(X)+2$. Degenerations with $\rho(X)+2$ and $\rho(X)+1$ non-Du Val points are investigated. ...
Added: October 17, 2014
Galkin S., Popov P., / Cornell University. Series math "arxiv.org". 2018. No. 1810.07001.
Let X(n) denote n-th symmetric power of a cubic surface X. We show that X(4)×X is stably birational to X(3)×X, despite examples when X(4) is not stably birational to X(3). ...
Added: October 19, 2018
Glutsyuk A., / Cornell University. Series math "arxiv.org". 2014. No. 1309.1843.
The famous conjecture of V.Ya.Ivrii (1978) says that in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero. In the present paper we study the complex algebraic version of Ivrii's conjecture for quadrilateral orbits in two dimensions, with reflections from complex algebraic curves. We present the complete ...
Added: September 29, 2013
Yuri Prokhorov, Documenta Mathematica 2010 Vol. 15 P. 843-872
We study Q-Fano threefolds of large Fano index. In
particular, we prove that the maximum possible Fano index is attained
only by the weighted projective space P(3,4,5,7). ...
Added: December 6, 2013
Prokhorov Y., Zaidenberg M., European Journal of Mathematics 2016 Vol. 2 No. 1 P. 262-282
We construct four different families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of the form Z ×A1, where Z is a quasiprojective variety. The affine cones over such a fourfold admit effective Ga-actions. Similar constructions of cylindrical Fano threefolds were done previously in the papers by Kishimoto ...
Added: November 27, 2015
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
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
Prokhorov Y., Shramov K., Mathematical Research Letters 2018 Vol. 25 No. 3 P. 957-972
We classify threefolds with non-Jordan birational automorphism groups. ...
Added: October 4, 2018
Perepechko A., Michałek M., Süß H., Mathematische Zeitschrift 2018 Vol. 290 No. 3-4 P. 1457-1478
We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant varieties of Segre–Veronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces. ...
Added: September 26, 2019
Prokhorov Y., Mori S., Известия РАН. Серия математическая 2019 Т. 83 № 3 С. 158-212
Росток экстремальной окрестности – это аналитический росток трехмерного многообразия с терминальными особенностями вдоль приведенной полной кривой, допускающий стягивание, слои которого не более чем одномерны. Цель настоящей статьи – дать обзор результатов, касающихся стягиваний с неприводимым центральным слоем, содержащих только одну негоренштейнову точку. ...
Added: June 4, 2019
I. Arzhantsev, Kaliman S., M. Zaidenberg, Advances in Mathematics 2024 Vol. 437 Article 109449
It was shown by Kaliman and Zaidenberg (2023) that the affine cones over flag manifolds and rational smooth projective surfaces are elliptic in the sense of Gromov. The latter remains true after successive blowups of points on these varieties. In the present article we extend this to smooth projective spherical varieties (in particular, toric varieties) successively ...
Added: December 17, 2023
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2013. No. 1307.5522.
This is an expanded version of my talk at the workshop ``Groups of Automorphisms in Birational and Affine Geometry'', October 29–November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. ...
Added: July 21, 2013
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
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017