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Derived categories of families of Fano threefolds
Algebraic Geometry. 2025. Vol. 12. No. 4. P. 519–574.
Kuznetsov A.
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.
Publication based on the results of:
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The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
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Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
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Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
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Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
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Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
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Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
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Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
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Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
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Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
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Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
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Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
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Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
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Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
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 ...
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Vasilev D., / Series arXiv "math". 2025.
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Доран Ч., Кацарков Л., Овчаренко М.А. et al., Труды Математического института им. В.А. Стеклова РАН 2025 Т. 328 С. 165–310
For each smooth Fano threefold, we construct a family of Landau–Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi–Yau varieties with proper superpotential maps; they admit open algebraic torus charts on which the superpotential function w restricts to a Laurent polynomial satisfying a deformation of the Minkowski ...
Added: May 5, 2025
Kuznetsov A. G., Prokhorov Y., Izvestiya. Mathematics 2025 Vol. 89 No. 3 P. 495–594
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds of higher Picard rank and with unprojections of complete intersection varieties. ...
Added: December 13, 2024
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
Guseva L., Journal de Mathématiques Pures et Appliquées 2023 Vol. 180 P. 1–46
We construct a full exceptional collection consisting of vector bundles in the derived category of coherent sheaves on the so-called Cayley Grassmannian, the subvariety of the Grassmannian Gr(3,7) parameterizing 3-subspaces that are annihilated by a general 4-form. The main step in the proof of fullness is a construction of two self-dual vector bundles which is obtained from two operations ...
Added: November 16, 2023