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$c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
Proceedings of the Steklov Institute of Mathematics. 2025. Vol. 326. P. 339–351.
Yunhyung C., Eunjeong L., Mikiya M., Seonjeong P.
The c1-cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a c1-preserving isomorphism between their integral cohomology rings. In this paper, we confirm the conjecture for smooth toric Fano varieties of Picard number 2.
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 ...
Added: September 1, 2026
Batanin M., White D., Journal of Pure and Applied Algebra 2024 Vol. 228 No. 6 Article 107570
Given a combinatorial (semi-)model category M and a set of morphisms C, we establish the existence of a semi-model category LCM satisfying the universal property of the left Bousfield localization in the category of semi-model categories. Our main tool is a semi-model categorical version of a result of Jeff Smith, that appears to be of ...
Added: December 26, 2025
Akhmet’ev P., Switzerland: Springer, 2025.
This book consists of a collection of articles dedicated to Valentin Poénaru, on topology and geometry in a broad sense. Poénaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this ...
Added: October 27, 2025
Абрамов А. С., Chernyshev V. L., Mikhaylets E. et al., / Series Social Science Research Network "Social Science Research Network". 2025.
Computer vision is one of the most relevant modern research areas with broad practical applications. However, traditional solutions based on deep learning have signicant limitations and can be misleading. Topological data analysis, on the other hand, is a modern approach to solving similar problems using mathematically deterministic methods of algebraic topology that reduce the risk ...
Added: September 23, 2025
Yunhyung C., Eunjeong L., Mikiya M. et al., Fields Institute Communications 2024 Vol. 89 P. 107–119
Fano Bott manifolds bijectively correspond to signed rooted forests with some equivalence relation. Using this bijective correspondence, we enumerate the isomorphism classes of Fano Bott manifolds and the diffeomorphism classes of indecomposable Fano Bott manifolds. We also observe that the signed rooted forests with the equivalence relation bijectively correspond to rooted triangular cacti. ...
Added: August 30, 2025
Chernyshev V. L., Pyatko D., Математические заметки 2023 Т. 113 № 4 С. 560–576
Получена асимптотика числа конечных положений случайного блуждания на ориентированном гамильтоновом метрическом графе. ...
Added: August 29, 2025
Yunhyung C., Eunjeong L., Mikiya M. et al., Journal of Symplectic Geometry 2023 Vol. 21 No. 3 P. 439–462
We prove that if there exists a c1-preserving graded ring isomorphism between integral cohomology rings of two Fano Bott manifolds, then they are isomorphic as toric varieties. As a consequence, we give an affirmative answer to McDuff’s question on the uniqueness of a toric structure on a Fano Bott manifold. ...
Added: August 29, 2025
Horiguchi T., Mikiya M., Sato T., Algebraic Combinatorics 2024 Vol. 7 No. 5 P. 1433–1451
The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled ...
Added: August 29, 2025
Черных Г. С., European Journal of Mathematics 2025 No. 11 Article 27
We prove that if a complex genus ϕ : U → R is rigid on SU-manifolds with a torus action then ϕ is the elliptic Krichever genus. ...
Added: August 29, 2025
Panov T., М.: МЦНМО, 2024.
Настоящее издание подготовлено на основе лекционных курсов «Введение в топологию», «Топология-1», «Топология-2» и «Теория гомологий», прочитанных автором на механико-математическом факультете МГУ, в Независимом московском университете и Новосибирском университете.
В первой части рассматриваются основы теории гомотопий: клеточные пространства, фундаментальная группа, накрытия, гомотопическая теория расслоений и высшие гомотопические группы.
Во вторую часть входит теория гомологий: симплициальные, сингулярные и клеточные ...
Added: January 15, 2025
Springer, 2024.
This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions. Contributions to this volume were written in connection to the thematic program Toric Topology and Polyhedral Products held ...
Added: January 15, 2025
Ayzenberg A., Beketov M., Magaj G., / Series arxiv:math.AT "arxiv Algebraic Topology". 2023.
In this paper we study the nerves of two types of coverings of a sphere $S^{d-1}$: (1) coverings by open hemispheres; (2) antipodal coverings by closed hemispheres. In the first case, nerve theorem implies that the nerve is homotopy equivalent to $S^{d-1}$. In the second case, we prove that the nerve is homotopy equivalent to ...
Added: October 5, 2023
Nikolay Konovalov, / Series "Working papers by Cornell University". 2022. No. 2209.03312.
Let $\mathsf{s}_0\mathsf{Lie}^r$ be the category of $0$-reduced simplicial restricted Lie algebras over a fixed perfect field of positive characteristic $p$. We prove that there is a full subcategory $\mathrm{Ho}(\mathsf{s}_0\mathsf{Lie}^r_{\xi})$ of the homotopy category $\mathrm{Ho}(\mathsf{s}_0\mathsf{Lie}^r)$ and an equivalence $\mathrm{Ho}(\mathsf{s}_0\mathsf{Lie}^r_{\xi})\simeq\mathrm{Ho}(\mathsf{s}_1\mathsf{CoAlg}^{tr})$. Here $\mathsf{s}_1\mathsf{CoAlg}^{tr}$ is the category of $1$-reduced simplicial truncated coalgebras; informally, a coaugmented cocommutative coalgebra $C$ is ...
Added: September 12, 2022
Nikolai Konovalov, / Series "Working papers by Cornell University". 2020. No. 2010.09097.
In this note we compare the fracture squares from genuine equivariant stable homotopy theory and the fracture squares which appear in the Goodwillie tower for the norm functor. ...
Added: September 12, 2022
Switzerland: Birkhauser/Springer, 2022.
The conference “Interactions between Representation Theory and Algebraic Geometry” was held at the University of Chicago on August 21–25, 2017. It brought together about 150 participants from several major universities in the USA and abroad, more than half of whom were junior mathematicians. It featured 21 talks by eminent mathematicians from the USA, Europe, and Asia on topics ...
Added: June 20, 2022
Elagin A. D., Lunts V., Journal of Algebra 2021 Vol. 569 P. 334–376
In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems. ...
Added: February 25, 2021
Gavrilovich M., Pimenov K., / Series math "arxiv.org". 2020.
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial set, in a certain formal sense, reminiscent of the Skorokhod space of semi-continuous functions; in particular, we show the geometric realisation functor factors through an endofunctor of ...
Added: October 29, 2020
Gavrilovich M., / Series math "arxiv.org". 2019.
We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reformulation of a number of classical notions in topology, e.g. continuity, limit of a map or a sequence along a filter, various notions of equicontinuity and uniform convergence of a ...
Added: August 26, 2020
Netay I. V., / Series math "arxiv.org". 2016.
It is well known that the two-parametric Todd genus and elliptic functions of level~$d$ define $n$-multiplicative Hirzebruch genera, if~$d$ divides~$n+1$.
Both these cases are particular cases of Krichever genera defined by the Baker--Akhiezer functions.
In this work the inverse problem is solved.
Namely, it is proved that only these families of functions define $n$-multiplicative ...
Added: October 19, 2016
Vassiliev V., Труды Математического института им. В.А. Стеклова РАН 2015 Т. 290 С. 211–225
The naturally topologized order complex of proper algebraic subsets in RP^2, defined by systems of quadratic forms, has rational homology of S^13. ...
Added: January 19, 2016