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Rationality over nonclosed fields of Fano threefolds with higher geometric Picard rank
Journal of the Institute of Mathematics of Jussieu. 2024. Vol. 23. No. 1. P. 207–247.
Alexander Kuznetsov, Prokhorov Y.
We prove rationality criteria over nonclosed fields of characteristic 00 for five out of six types of geometrically rational Fano threefolds of Picard number 11 and geometric Picard number bigger than 11 . For the last type of such threefolds, we provide a unirationality criterion and construct examples of unirational but not stably rational varieties of this type.
Publication based on the results of:
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
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Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
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Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
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Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
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Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
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Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
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Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
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Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
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Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
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Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
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Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
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Ключников И. К., Saakyan T. V., Финансовый журнал 2025 Т. 17 № 1 С. 74–91
Subject. Rationality and efficiency of budgeting state subsidies to business entities. Objectives. To develop a science-based system for assessing the rationality and effectiveness of the process of state subsidization of business entities. Results. The interrelation of rationality and efficiency of the process of budgeting subsidies to business entities is substantiated. Determination of the logic of ...
Added: June 1, 2026
Кырма В. В., Орлова Е. О., Rozmainsky I. V., Журнал институциональных исследований 2025 Т. 17 № 3 С. 136–156
In this paper, we conducted a study of the prevalence of cheating among university students and analyzed the factors contributing to this phenomenon. Cheating is a form of opportunism, when an individual chooses a strategy to achieve success through deception, manipulation, or forgery. The research was carried out on the basis of a survey created ...
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Loginov K., Przyjalkowski V., Trepalin A., Труды Математического института им. В.А. Стеклова РАН 2025 Т. 329 С. 132–164
We introduce and study the notion of G-coregularity of algebraic varieties endowed with an action of a finite group G. We compute the G-coregularity of smooth del Pezzo surfaces of degree at least 6, and give a characterization of groups that can act on conic bundles with G-coregularity 0. We describe the relations between the notions of G-coregularity, G-log ...
Added: September 4, 2025
Emerging Adults’ Autonomy in Romantic Narrative Identities: Choices Between Emotions and Rationality
Victoria G. Yerofeyeva, Ekaterina M. Tsyganova, Bochaver A. A., Trends in Psychology 2025
This study examines how emerging adults define autonomy through their roman
tic relationship choices. Emerging adulthood provides a lot of opportunities to try
different things, but the diversity of alternatives makes it difficult to choose. Under
these conditions, autonomy becomes a necessary personal characteristic. We set
out to examine how young people construct romantic narratives identities based
on the characteristics ...
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Azhimov F., Pruzhinin B. I., Zhukova O. et al., М.: РОССПЭН, 2024.
Коллективная монография, посвященная 80-летию известного российского философа-эпистемолога Б. И. Пружинина, представляет основные тематические векторы его творчества – наука, рациональность, эпистемологический стиль русской философии, многообразие культур – на пересечении мнений, высказанных российскими и зарубежными философами (коллегами и друзьями юбиляра) на круглых столах. Стержневой темой публикуемых дискуссий стала концепция культурно-исторической эпистемологии: участники обсуждали ее философско-методологический потенциал в ...
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Poddiakov A., Human Arenas. An Interdisciplinary Journal of Psychology, Culture, and Meaning 2026 Vol. 9 No. 2 P. 1262–1291
The status of the axioms of transitivity of dominance (“if x dominates y and y dominates z, then x dominates z” and “if a person prefers A to B and B to C, then that person should prefer A to C”) as key components of rationality is discussed. The discussion is conducted in the context ...
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Kanaeva N., Вопросы философии 2024 № 7 С. 139–149
The paper presented to the reader’s attention pursues two goals. The first is a substantiation of the productivity of the concept “epistemic culture” (hereinafter – EC) as a tool of historico-philosophical intercultural research by the example of its application to the interpretation of the meanings of Indian logico-epistemological texts. The second is a demonstration of ...
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Белов М. Д., Социология власти 2024 Т. 36 № 1 С. 29–43
This article is devoted to the consideration of rationality as one of the key characteristics of Michel Foucault’s concept of governmentality and related contradictions both inside and outside Foucauldian theory. Using risk theory, the author explores the possibility of the existence of multiple rationality in governmentality and offers a solution to the contradiction within Foucauldian ...
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Shamarina E., В кн.: Третий Международный Конгресс Русского общества истории и философии науки «ПОСЛЕ ПОСТПОЗИТИВИЗМА». Сборник научных статей.: М.: Издательство РОИФН, 2022. С. 681–684.
Michael Friedman made an attempt to combine Kantian transcendental philosophy and Kuhn's historiographical model in a view of changes in science. His idea of a rational revision of scientific principles contrasts with Kuhn's idea of the existence of universal sets of values that ensure scientific progress. Friedman appeals to philosophical developments of the metatheoretical level ...
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Schedrina I., Вопросы философии 2023 № 9 С. 162–166
The article actualizes the historical and philosophical ideas of P.P. Gaidenko in the context of modern problems related to ecology, nature, and man in the surrounding world. The author refers to the concept of types of scientific rationality, emphasizing a unique niche in the history and philosophy of science, which is occupied by the scientific ...
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