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Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
Journal of Algebra. 2013. Vol. 374. P. 104–121.
We show that every Picard rank one smooth Fano threefold has a weak Landau–Ginzburg model coming from a toric degeneration. The fibers of these Landau–Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau–Ginzburg model coming from a toric degeneration.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Chernov A., European Journal of Mathematics 2026 Vol. 12 Article 48
An induced additive action on a projective variety is a regular action of the group G_a^n on X in P^n with an open orbit that can be extended to a regular action on P^n. Such actions are known to correspond to pairs (A, U), where A is a local algebra and U is a generating subspace lying in the maximal ideal. This paper ...
Added: August 19, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 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
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
Basalaev A., Journal of Geometry and Physics 2025 Vol. 215 Article 105538
The results of A.~Chiodo, Y.~Ruan and M.~Krawitz associate the mirror partner Calabi--Yau variety $X$ to a Landau--Ginzburg orbifold $(f,G)$ if $f$ is an invertible polynomial satisfying Calabi--Yau condition and the group $G$ is a diagonal symmetry group of $f$.
In this paper we investigate the Landau--Ginzburg orbifolds with a Klein quartic polynomial $f = x_1^3x_2 + ...
Added: November 27, 2025
Kasprzyk A., Katzarkov Ludmil, Przyjalkowski Victor et al., Taiwanese Journal of Mathematics 2025 Vol. 29 No. 6 P. 1411–1494
A new structure connecting toric degenerations of smooth Fano threefolds by projections was introduced by I. Cheltsov et al. in “Birational geometry via moduli spaces”. Using Mirror Symmetry, these connections were transferred to the side of Landau–Ginzburg models, and a nice way to connect the Picard rank one Fano threefolds was described. We apply this ...
Added: October 30, 2025
Shafarevich A., Research in the Mathematical Sciences 2025 Vol. 12 No. 1 Article 6
We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the cases when the dimension is equal to 2 or the divisor class group is Z. ...
Added: March 10, 2025
Kikteva V., Sbornik Mathematics 2024 Vol. 215 No. 10 P. 1351–1373
We obtain a criterion for the automorphism group of an affine toric variety to be connected, stated in combinatorial terms and in terms of the divisor class group of the variety. We describe the component group of the automorphism group of a nondegenerate affine toric variety. In particular, we show that the number of connected components of ...
Added: January 27, 2025
Roman Avdeev, Vladimir Zhgoon, / Series arXiv "math". 2024. No. 2312.03377.
Given a connected reductive algebraic group G and a spherical G-variety X, a B-root subgroup on X is a one-parameter additive group of automorphisms of X normalized by a Borel subgroup B⊂G. We obtain a complete description of all B-root subgroups on a certain open subset of X. When X is horospherical, we extend the construction of standard B-root subgroups introduced earlier by Arzhantsev and Avdeev for affine X and obtain a ...
Added: December 17, 2024
Varolgunes U., Polishchuk A., Mathematische Annalen 2024 Vol. 388 P. 2331–2386
We consider Takahashi’s categorical interpretation of the Berglund–Hubsch mirror symmetry conjecture for invertible polynomials in the case of chain polynomials. Our strategy is based on a stronger claim that the relevant categories satisfy a recursion of directed -categories, which may be of independent interest. We give a full proof of this claim on the B-side. On ...
Added: December 2, 2024
Kikteva V., Математический сборник 2024 Т. 215 № 10 С. 89–113
We obtain a criterion for the automorphism group of an affine toric variety to be connected in combinatorial terms and in terms of the divisor class group of the variety. The component group of the automorphism group of a non-degenerate affine toric variety is described. In particular, we show that the number of connected components ...
Added: September 30, 2024