?
Deformations and BBF form on non-Kahler holomorphically symplectic manifolds
Verbitsky M., Kurnosov N.
Publication based on the results of:
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
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
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Serge Lvovski, Arnold Mathematical Journal 2025 Vol. 11 No. 2 P. 133–153
Suppose that 𝐹 is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive selfintersection. We prove that if there exists a non-constant meromorphic function on 𝐹, then the field of meromorphic functions on 𝐹 is isomorphic to the field of rational functions in one or two variables over ...
Added: August 13, 2025
Bogomolov F. A., Déev R., Verbitsky M., Advances in Mathematics 2022 Vol. 405 Article 108479
Let (M,I,Ω) be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration π:M↦X, and η a closed form of Hodge type (1,1)+(2,0) on X. We prove that Ω′:=Ω+π∗η is again a holomorphically symplectic form, for another complex structure I′, which is uniquely determined by Ω′. The corresponding deformation of complex structures is called "degenerate twistorial deformation". The map π is holomorphic with respect to this new ...
Added: November 29, 2022
Bogomolov F. A., Kurnosov N., Kuznetsova A. et al., International Mathematics Research Notices 2022 Vol. 2022 No. 16 P. 12302–12341
We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works by D. Guan and the 1st author. Any such manifold Q of dimension 2n−2 is obtained as a finite degree n2 cover of some non-Kähler manifold WF, which we call the base of Q. We show that the algebraic reduction of Q and its base is the projective space of ...
Added: November 29, 2022
Rogov V., / Series arXiv "math". 2019.
Let X be a compact Kähler manifold with vanishing Riemann curvature. We prove that there exists a manifold X′, deformation equivalent to X, which is not an analytification of any projective variety, if and only if H^0(X, Ω^2)≠0. Using this, we recover a recent theorem of Catanese and Demleitner, which states that a rigid smooth quotient of a complex torus ...
Added: August 19, 2020
Verbitsky M., Kamenova L., / Series arXiv "math". 2019.
Let M be a holomorphic symplectic Kähler manifold equipped with a Lagrangian fibration π with compact fibers. The base of this manifold is equipped with a special Kähler structure, that is, a Kähler structure (I,g,ω) and a symplectic flat connection ∇ such that the metric g is locally the Hessian of a function. We prove that any Lagrangian subvariety Z⊂M which intersects smooth fibers of π and smoothly projects ...
Added: June 9, 2019
Verbitsky M., Mehrotra S., Markman E., European Journal of Mathematics 2019 Vol. 5 No. 3 P. 964–1012
Let S be a K3 surface and M a smooth and projective 2n-dimensional moduli space of stable coherent sheaves on S. Over 𝑀×𝑀 there exists a rank 2𝑛−2 reflexive hyperholomorphic sheaf 𝐸_𝑀, whose fiber over a non-diagonal point (𝐹_1, 𝐹_2) is Ext^1_𝑆 (𝐹_1, 𝐹_2). The sheaf 𝐸_𝑀 can be deformed along some twistor path to a sheaf 𝐸_𝑋 over the Cartesian square 𝑋×𝑋 of every Kähler manifold X deformation equivalent to M. We prove that 𝐸_𝑋 is ...
Added: March 11, 2019
Boldyrev K., Малкин Б. З., Абишев Н. М. et al., Physical Review B: Condensed Matter and Materials Physics 2017 Vol. 96 No. 1 P. 014116-1–014116-13
We construct a distribution function of the strain-tensor components induced by point defects in an elastically anisotropic continuum, which can be used to account quantitatively for many effects observed in different branches of condensed matter physics. Parameters of the derived six-dimensional generalized Lorentz distribution are expressed through the integrals computed over the array of strains. ...
Added: February 8, 2019