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Когерентные пучки, классы Чженя и суперсвязности на компактных комплексно-аналитических многообразиях
Известия РАН. Серия математическая. 2023. Т. 87. № 3. С. 23–55.
Bondal A. I., Rosly A. A.
We construct a twist-closed enhancement of the category Dbcoh(X), the bounded derived category of complexes of OX-modules with coherent cohomology, by means of the DG-category of ∂¯-superconnections. Then we apply the techniques of ∂¯-superconnections to dene Chern classes and Bott–Chern classes of objects in the category, in particular, of coherent sheaves.
Buryak A., Tessler R., Troshkin M., Journal of Geometry and Physics 2026 Vol. 223 Article 105783
We give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to . We prove that the resulting sequence of partition functions, depending on , is a tau-sequence of ...
Added: June 19, 2026
Buryak A., Rossi P., Communications in Mathematical Physics 2025 Vol. 406 Article 205
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second has the advantage of being very explicit. The Poisson operator of the DR hierarchy is , where is the metric ...
Added: June 19, 2026
Cham: Springer Publishing Company, 2026.
The four-volume set LNCS 16483-16486 constitutes the refereed conference proceedings of the 48th European Conference on Information Retrieval, ECIR 2026, held in Delft, The Netherlands, during March 29–April 2, 2026.
The 46 full papers and 37 short papers presented together with 10 findings papers, 9 reproducibility papers, 17 resource papers, 11 workshop papers, 7 tutorial papers, ...
Added: June 18, 2026
Poddiakov A., Троицкий вариант. Наука 2026 № 12 С. 24–25
В научно-популярной заметке представлен обзор содержания поста филдсовского медалиста Тимоти Гауэрса о возможностях ИИ в математике и содержания комментариев под постом. Обзор сделан в основном чат-ботом DeepSeek. В заключение обсуждается возможность не только решения задач искусственным интеллектом, но и их постановки. ...
Added: June 18, 2026
Garzón J., Mora Rodríguez J., Moreno-Franco H. A., Applied Mathematics and Optimization 2026 Vol. 94 No. 10 P. 1–43
We study an optimal extraction problem where the agent’s actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, evolve according to a drifted Brownian motion with jumps. The agent’s primary aim is to identify an optimal extraction strategy ...
Added: June 17, 2026
Nesterov A. S., Журнал Новой экономической ассоциации 2026
В этой статье рассматривается целевой приём в вузы в России с точки зрения науки об устройстве рынков сочетания и экономических механизмов (matching market and mechanism design), ключевого направления современной теории игр. Мы изучаем механизм целевого приёма -- набор правил, по которым устраивается трёхстороннее сочетание между абитуриентом, заказчиком и образовательной программой. Используемый в России механизм имеет ...
Added: June 16, 2026
Kh. Kh. Abdullin, D. B. Mokeev, D. S. Taletskii, Mathematical notes 2026 Vol. 119 No. 1 P. 3–7
By the Ramsey number R(K1,s,Pt) one means the least positive integer n such that, for every n-vertex graph G, the following condition holds: either G contains a vertex of degree at least s or the complement of G contains a simple t-path. In this paper, we fi nd precise values of R(K1,s,Pt) for certain values ...
Added: June 10, 2026
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Mironov M., European Journal of Mathematics 2021 Vol. 7 No. 3 P. 1182–1208
We consider the bounded derived category of Sk-equivariant coherent sheaves on (Pn)k. The goal of this paper is to construct in this category a rectangular Lefschetz exceptional collection when this is possible, or a minimal Lefschetz exceptional collection when a rectangular one does not exist. The main results of the paper include the construction of a rectangular ...
Added: March 4, 2024
Katzarkov L. V., Karzhemanov I., / Series math "arxiv.org". 2023. No. 2310.13319.
Added: October 31, 2023
Lu L., Piontkovski D., International Mathematics Research Notices 2023 Vol. 2023 No. 3 P. 2446–2473
Let A be a finitely presented associative monomial algebra. We study the category qgr(A) which is a quotient of the category of graded finitely presented A-modules by the finite-dimensional ones. As this category plays a role of the category of coherent sheaves on the corresponding noncommutative variety, we consider its bounded derived category. We calculate ...
Added: April 28, 2023
Kuznetsov A., International Mathematics Research Notices 2021 Vol. 2021 No. 12 P. 9262–9339
We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a ...
Added: December 12, 2022
Bergh D., Gorchinskiy S., Larsen M. et al., Journal of Algebraic Geometry 2021 Vol. 30 P. 685–757
Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases that these two measures coincide. This implies, in particular, ...
Added: November 17, 2021
Fonarev A., Transformation Groups 2020
We construct a minimal Lefschetz decomposition of the bounded derived category of coherent sheaves on the isotropic Grassmannian IGr(3, 7). Moreover, we show that IGr(3, 7) admits a full exceptional collection consisting of equivariant vector bundles. ...
Added: September 27, 2021
Elagin A. D., Lunts V., Schnürer O., Moscow Mathematical Journal 2020 Vol. 20 No. 2 P. 277–309
We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, thereby answering a question of Iyama. More generally, we prove this statement for any algebra over a perfect field that is finite over its center and whose center is finitely generated ...
Added: May 11, 2020
Dimitrov G., Katzarkov L. V., Selecta Mathematica, New Series 2019 Vol. 25:45 P. 1–60
In this paper we introduce new categorical notions and give many examples. In an
earlier paper we proved that the Bridgeland stability space on the derived category of
representations of K(l), thel-Kronecker quiver, is biholomorphic toC×Hfor l ≥ 3. In
the present paper we define a new notion of norm, which distinguishes {Db(K(l))}l≥2.
More precisely, to a triangulated category ...
Added: November 1, 2019
Antipov M., Zvonareva A., Mathematische Zeitschrift 2022 Vol. 301 No. 2 P. 1963–1981
In this paper the class of Brauer graph algebras is proved to be closed
under derived equivalence. For that we use the rank of the maximal torus of the identity
component of the group of outer automorphisms Out0(A) of a symmetric stably biserial
algebra A. ...
Added: November 1, 2019
Elagin A., Lunts V. A., Sbornik Mathematics 2018 Vol. 209 No. 12 P. 1756–1782
Let R be a commutative Noetherian ring such that X=SpecR is connected. We prove that the category D^b(cohX) contains no proper full triangulated subcategories which are strongly generated. We also bound below the Rouquier dimension of a triangulated category T, if there exists a triangulated functor T→D^b(cohX) with certain properties. Applications are given to the cohomological annihilator of R and to point-like objects in T. ...
Added: October 13, 2019
Antipov M., Звонарёва А. О., Journal of Mathematical Sciences 2014 Vol. 202 No. 3 P. 333–345
In this paper, all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 are described, using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an application, all two-term tilting complexes over a Brauer star algebra are described and their endomorphism rings are ...
Added: December 25, 2018
Finkelberg M. V., Braverman A., / Series arXiv "math". 2018.
In arXiv:1807.09038 we formulated a conjecture describing the derived category D-mod(Gr_GL(n)) of (all) D-modules on the affine Grassmannian of the group GL(n) as the category of ind-coherent sheaves on a certain stack (it is explained in loc. cit. that this conjecture "follows" naturally from some heuristic arguments involving 3-dimensional quantum field theory). In this paper we prove a ...
Added: December 3, 2018
Guseva L., / Series math "arxiv.org". 2018.
We construct a full exceptional collection of vector bundles in the bounded derived category of
coherent sheaves on the Grassmannian IGr(3,8) of isotropic 3-dimensional subspaces in a symplectic vector
space of dimension 8. ...
Added: October 19, 2018
Bondal A. I., Bodzenta-Skibinska A., Advances in Mathematics 2018 Vol. 323 P. 226–278
Given a relatively projective birational morphism f : X → Y
of smooth algebraic spaces with dimension of fibers bounded
by 1, we construct tilting relative (over Y) generators TX,f
and S_X,f in D^b(X). We develop a piece of general theory of
strict admissible lattice filtrations in triangulated categories
and show that D^b(X) has such a filtration L where the ...
Added: May 2, 2018