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Néron–Severi Lie Algebra, Autoequivalences of the Derived Category, and Monodromy
Moscow Mathematical Journal. 2022. Vol. 22. No. 4. P. 705–739.
Lunts V.
Let X be a smooth complex projective variety. The group of autoequivalences of the derived category of X acts naturally on its singular cohomology H(X; Q) and we denote by Geq(X) GL(H(X; Q)) its image. Let Geq(X) GL(H(X; Q) be its Zariski closure. We study the relation of the Lie algebra LieGeq(X) and the Neron{Severi Lie
algebra gNS(X) End(H(X; Q)) in case X has trivial canonical line bundle.
At the same time for mirror symmetric families of (weakly) Calabi-Yau varieties we consider a conjecture of Kontsevich on the relation between the monodromy of one family and the group Geq(X) for a very
general member X of the other family.
Publication based on the results of:
Domrin V. I., Malova H. V., V. Yu. Popov et al., Cosmic Research 2026 Vol. 64 No. 2 P. 238–252
During magnetospheric perturbations a relatively thin current sheet with thickness about several
proton gyroradii forms in the Earth’s magnetotail. In a framework of the kinetic model describing current
sheet thinning in the magnetotail, the processes of its formation are investigated depending on the normal
magnetic field magnitude which affects both the current sheet structure and particle dynamics within ...
Added: April 27, 2026
Tsareva O. O., Malova H. V., V. Yu. Popov et al., Plasma Physics Reports 2026 Vol. 52 No. 2 P. 179–185
The influence of asymmetry of plasma sources on the structure and spatial localization of a superthin
current sheet (STCS) supported by demagnetized electrons is studied using a self-consistent model. The
simulation takes into account the presence of a single plasma source in the northern hemisphere, which
makes the plasma flow asymmetric. It is demonstrated that the asymmetry of ...
Added: April 27, 2026
Pochinka O., Yakovlev E., Shmukler V., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Kazaryan M., Lando S., Kodaneva N., Journal of Geometry and Physics 2026 No. 225 Article 105841
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm ...
Added: April 23, 2026
Kychkin A., Chernitsin I., Прикладная информатика 2026 Т. 21 № 1 С. 40–58
The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological ...
Added: April 23, 2026
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Polynomials of least deviation from zero play an important role in the theory and practice of numerical methods. They can be used to solve problems of optimizing the properties of various computational algorithms. Our work is devoted to the study of polynomials of least deviation from zero on a ray in the exponential norm. In ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Petrov I., Doklady Mathematics 2026 Vol. Volume 112 P. S103–S110
This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent ...
Added: April 17, 2026
A. V. Pereskokov, Theoretical and Mathematical Physics 2026 Vol. 226 No. 3 P. 470–484
We consider the spectral problem for a hydrogen atom in orthogonal electric and magnetic fields with
an additional self-consistent field. We obtain an asymptotic expansion of self-consistent energy levels.
We find an asymptotic expansion of asymptotic eigenfunctions near the sphere |q| = 2. We calculate the
asymptotics of their norm in the space L2(R3). ...
Added: April 12, 2026
Kolachev N., Адамский А. И., Drozdov D. et al., Моделирование и анализ данных 2026 Т. 16 № 1 С. 157–176
Context and relevance. Despite the widespread adoption of the competency-based approach in higher education, a gap remains between the understanding of competence as a dynamic process and the tools available for its design and management. Dominant practices of learning outcomes assessment rely on static “snapshots,” which limits the possibilities for forecasting and purposeful development of competence. ...
Added: April 10, 2026
Zvereva V., Вопросы экономики 2026 № 4 С. 100–129
This paper examines the hypothesis of asymmetric responses of bank interest rates to restrictive and accommodative monetary policy conducted by the Bank of Russia across different market segments, industries, and macroregions over the period 2017—2025. Using a Markov-switching error-correction model, the paper estimates the effects of monetary policy shocks, households’ inflation expectations, firms’ price expectations, ...
Added: April 8, 2026
Petropavlovsky S., Turkel E., Journal of Computational Physics 2026 Vol. 558 Article 114880
We propose a method for the numerical computation of the 3D time-harmonic scattering about objects of complex shape. Our approach relies on the method of difference potentials combined with the lacunae-based integration of the Helmholtz equation. The former allows to handle curvilinear boundaries of scattering shapes on regular Cartesian grids with no loss of accuracy. ...
Added: April 6, 2026
Romanov I., Шамаев А. С., Математические заметки 2026 Т. 119 № 3 С. 426–432
The existence of a propagation front is proved in the Cauchy problem for a multidimensional wave equation with integral memory and a Rabotnov kernel, which is considered in a certain special case. ...
Added: April 6, 2026
Anna S. Bodrova, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 113 No. 4 Article 045403
We investigate the diffusion coefficients and mean-squared displacements in a polydisperse granular gas in
a homogeneous cooling state by considering the roughness of the particles. We study their dependence on the
normal and tangential restitution coefficients. We show that the motility of particles is strongly affected by their
mechanical properties and surface characteristics. ...
Added: April 5, 2026
Shvedov A. S., Математические заметки 2026 Т. 119 № 4 С. 616–623
В настоящей работе изучается некооперативная игра, в которой фирмы-лидеры конкурируют между собой, выбирая объемы выпуска, и фирмы-последователи конкурируют между собой, также выбирая объемы выпуска. Информация о средних предельных затратах является общедоступной, но текущие предельные затраты фирмы известны только самой фирме. Для этой игры найдены равновесные объемы выпуска. ...
Added: April 3, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Tuzhilin M., Moscow University Mathematics Bulletin 2025 Vol. 80 P. 335–341
Relations between average clustering coefficient and global clustering coefficient, local efficiency, radiality, closeness, betweenness, and stress centralities were obtained for simple graphs. ...
Added: April 1, 2026
Kuznetsov A., Algebraic Geometry 2025 Vol. 12 No. 4 P. 519–574
We construct S-linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations X/S with relative Picard rank 1 and rational geometric fibers and discuss how the structure of components of these decompositions is related to rationality properties of X/S. ...
Added: November 29, 2025
Kuznetsov A., Shinder E., Inventiones Mathematicae 2025 Vol. 239 P. 377–430
Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree d∈{2,3,4,5}d∈{2,3,4,5} and crepant categorical resolutions of the nontrivial components of the derived categories of nodal del Pezzo threefolds of degree d=1d=1 can be smoothly deformed to the nontrivial components of the derived categories of prime ...
Added: November 29, 2025
Amburg N., Tolstukhin I., Journal of Geometry and Physics 2025 Vol. 211 Article 105436
We study the three-point quantum sl2 Gaudin model. In this case the compactification of the parameter space is M0,4(C)‾, which is the Riemann sphere. We analyze sphere coverings by the joint spectrum of the Gaudin Hamiltonians treating them as algebraic curves. We write equations for these curves as determinants of tridiagonal matrices and deduce some ...
Added: March 8, 2025
Efimov A., , in: European Congress of Mathematics Portorož, 20–26 June, 2021.: EMS Press, 2023. P. 535–551.
This is a short overview of the author’s results related to the notion of a smooth categorical compactification. We cover the construction of a categorical smooth compactification of the derived categories of coherent sheaves, using the categorical resolution of Kuznetsov and Lunts. We also mention examples of homotopically finitely presented DG categories which do not ...
Added: December 6, 2023