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## Группы гомологий пространств нерезультантных систем квадратичных полиномов в R^3

Известия РАН. Серия математическая. 2016. Т. 80. № 4. С. 163-184.

Rational homology groups of spaces of non-resultant (that is, having only trivial common zeros) systems of homogeneous quadratic polynomial systems in R^3 are calculated

Vassiliev V., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2017 Т. 477 № 6 С. 637-640

The stabilization of cohomology rings of spaces of non-resultant homogeneous polynomial systems of growing degree in $\R^3$ is studied. The rational stable cohomology rings are explicitly calculated, and the instant of stabilization is estimated ...

Added: December 27, 2017

V.A. Vassiliev, Arnold Mathematical Journal 2015 Vol. 1 No. 3 P. 233-242

The resultant variety in the space of systems of homogeneous polynomials of some given degrees consists of such systems having non-trivial solutions. We calculate the integer cohomology groups of all spaces of non-resultant systems of polynomials R2→R, and also the rational cohomology rings of spaces of non-resultant systems and non-m-discriminant polynomials in C2. ...

Added: January 19, 2016

V.A.Vassiliev, Doklady Mathematics 2018 Vol. 98 No. 1 P. 330-333

Stable rational cohomology groups of spaces of non-resultant homogeneous polynomial systems of growing degree in R^n are calculated ...

Added: December 7, 2018

Angella D., Tomassini A., Verbitsky M., / Cornell University. Series arXiv "math". 2016.

We study cohomological properties of complex manifolds. In particular, we provide an upper bound for the Bott-Chern cohomology in terms of Betti numbers for compact complex surfaces, according to the dichotomy b1 even or odd. In higher dimension, a similar result is obtained at degree 1 under additional metric conditions (see Theorem 2.4). ...

Added: May 14, 2016

Buryak A., Shadrin S., Zvonkine D., Journal of the European Mathematical Society 2016 Vol. 18 No. 12 P. 2925-2951

We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus g curves with n marked points. ...

Added: September 27, 2020

Chebochko N.G., / Cornell University. Series math "arxiv.org". 2017. No. 1712.01810.

The description of global deformations of Lie algebras is important since it is related to unsolved problem of the classification of simple Lie algebras over a field of small characteristic.
In this paper we study global deformations of Lie algebras of type ${D}_{l}$ over an algebraically closed field K of characteristic 2. It is proved that ...

Added: December 8, 2017

Fedor Bogomolov, Tschinkel Y., Communications on Pure and Applied Mathematics 2013 Vol. 66 No. 9 P. 1335-1359

We explore connections between birational anabelian geometry and abstract projective geometry. One of the applications is a proof of a version of the birational section conjecture. ...

Added: December 27, 2013

Podkopaev O., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2018 Т. 5(63) № 4 С. 631-636

The goal of this note is to give a proof of the following proposition. Let π be a profinite group and K∗ be a bounded complex of discrete Fp[π]-modules. Assume all Hi (K∗) are finite abelian groups. Then there exists a quasiisomorphism L∗ −→ K∗, where L∗ is a bounded complex of discrete Fp[π]-modules such ...

Added: April 18, 2021

Victor A. Vassiliev, Combinatorica 2018 Vol. 38 No. 5 P. 1239-1249

We describe the homotopy types of complexes of partite graphs and hypergraphs with a fixed set of vertices covered by their edges ...

Added: December 27, 2017

V.A.Vassiliev, European Journal of Combinatorics 2020 Vol. 86 P. 1-7

The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of Goresky–MacPherson approach to similar homology calculations is proposed. ...

Added: March 21, 2020

Брудный Ю. А., Зайденберг М. Г., Лин В. Я. et al., Успехи математических наук 2019 Т. 74 № 5 С. 170-180

A detailed review of the scientific activities of the remarkable domestic mathematician E. A. Gorin and his results ...

Added: March 17, 2020

Esterov A. I., Voorhaar A., Geometric and Functional Analysis 2017 Vol. 27 No. 1 P. 33-66

We construct a certain $F_2$-valued analogue of the mixed volume of lattice polytopes. This 2-mixed volume cannot be defined as a polarization of any kind of an additive measure, or characterized by any kind of its monotonicity properties, because neither of the two makes sense over $F_2$. In this sense, the convex-geometric nature of the ...

Added: February 27, 2017

Abramov Y. V., / Cornell University. Series math "arxiv.org". 2011. No. arXiv:1111.4974v1.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables ...

Added: June 28, 2012

Lopatkin V., Kolesnikov P., Alhussein H., / Cornell University. Series arXiv "math". 2022.

We apply discrete algebraic Morse theory to the computation of Hochschild cohomologies of associative conformal algebras. As an example, we evaluate the dimensions of the universal associative conformal envelope U(3) of the Virasoro Lie conformal algebra relative to the associative locality N=3 on the generator with scalar coefficients. ...

Added: May 5, 2022

V.A. Vassiliev, Philosophical Transactions of the Royal Society of London. Series A: Mathematical and Physical Sciences 2001 Vol. 359 No. 1784 P. 1343-1364

I shall describe the recent progress in the study of cohomology rings of spaces of knots in R^n, H^∗({knots in R^n}), with arbitrary n>23. ‘Any dimensions’ in the title can be read as dimensions n of spaces R^n, as dimensions i of the cohomology groups H^i, and also as a parameter for different generalizations of ...

Added: May 25, 2010

Buryak A., Hernandez Iglesias F., Shadrin S., Epijournal de Geometrie Algebrique 2022 Vol. 6 Article 8595

We propose a conjectural formula for DR_g(a,−a)\lambda_g and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Guéré and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way. ...

Added: September 14, 2022

Kurnosov N., Soldatenkov A., Verbitsky M., Advances in Mathematics 2019 Vol. 351 P. 275-295

Let M be a simple hyperkähler manifold. Kuga-Satake
construction gives an embedding of H^2(M, C) into the
second cohomology of a torus, compatible with the Hodge
structure. We construct a torus T and an embedding of the
graded cohomology space H^•(M, C) → H^{•+l}(T, C) for some
l, which is compatible with the Hodge structures and the
Poincaré pairing. Moreover, this ...

Added: June 3, 2019

V.A.Vassiliev, Doklady Mathematics (Springer, Germany) 2018 Vol. 98 No. 3 P. 629-633

We calculate homology groups with certain twisted coefficients of configuration spaces of projective spaces. This completes a calculation of rational homology groups of spaces of odd maps of spheres S^m \to S^M, m<M, and of the stable homology of spaces of non-resultant polynomial maps R^{m+1} -> R^{M+1}. Also, we calculate the homology of spaces of Z_r-equivariant maps ...

Added: January 9, 2019

Victor A. Vassiliev, Journal of Knot Theory and Its Ramifications 2016 Vol. 25 No. 12

The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constructing similar homotopy invariants of links in non-orientable manifolds. ...

Added: November 15, 2016

Guere J., Rossi P., Buryak A., Geometry and Topology 2019 Vol. 23 No. 7 P. 3537-3600

We present a family of conjectural relations in the tautological ring of the moduli spaces of stable curves which implies the strong double ramification/Dubrovin–Zhang equivalence conjecture introduced by the authors with Dubrovin. Our tautological relations have the form of an equality between two different families of tautological classes, only one of which involves the double ...

Added: April 21, 2020

Przyjalkowski V., Shramov K., Collectanea Mathematica 2020 Vol. 71 P. 549-574

We give lower bounds for Hodge numbers of smooth well formed Fano weighted complete intersections. In particular, we compute their Hodge level, that is, the maximal distance between non-trivial Hodge numbers in the same row of the Hodge diamond. This allows us to classify varieties whose Hodge numbers are like that of a projective space, ...

Added: November 13, 2020

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624

Added: February 27, 2013

Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013

Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...

Added: February 5, 2014