?
A conjectural formula for DRg(a,−a)λg
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.
Васильев Д. А., Siberian Mathematical Journal 2023 Vol. 64 No. 3 P. 525-541
We construct an infinite series of irreducible components of the moduli space of stable rank 3 sheaves on P3 with the zero first Chern class and establish the rationality of the components of this series. We also prove the rationality of the irreducible components of the moduli space of stable rank 2 sheaves on P3 belonging to an infinite subseries of the series ...
Added: May 29, 2023
Arsie A., Buryak A., Lorenzoni P. et al., Communications in Mathematical Physics 2023 Vol. 397 P. 141-197
In this paper, we generalize the Givental theory for Frobenius manifolds and cohomological field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a notion of Givental cone for flat F-manifolds, and we provide a generalization of the Givental group as a matrix loop group acting on them. We show that this action is transitive on semisimple flat F-manifolds. We then extend this ...
Added: December 8, 2022
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
Alexandrov A., Basalaev A., Buryak A., International Mathematics Research Notices 2023 Vol. 2023 No. 17 P. 14840-14889
We present a construction of an open analogue of total descendant and total ancestor potentials via an “open version” of Givental’s action. Our construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a unit. We show that the open total descendant potentials we define ...
Added: September 14, 2022
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
Michael Finkelberg, Matviichuk M., Polishchuk A., Journal of Algebraic Geometry 2023 Vol. 32 No. 1 P. 183-237
We study the elliptic zastava spaces, their versions (twisted, Coulomb, Mirković local spaces, reduced) and relations with monowalls moduli spaces and Feigin-Odesskiı̆ moduli spaces of G-bundles with parabolic structure on an elliptic curve. ...
Added: February 26, 2023
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
Roman Avdeev, Cupit-Foutou S., Transformation Groups 2018 Vol. 23 No. 2 P. 299-327
We give a combinatorial description of all affine spherical varieties with prescribed weight monoid Γ. As an application, we obtain a characterization of the irreducible components of Alexeev and Brion’s moduli scheme M_Γ for such varieties. Moreover, we find several sufficient conditions for M_Γ to be irreducible and exhibit several examples where M_Γ is reducible. ...
Added: October 17, 2017
Брауэр О., Buryak A., Функциональный анализ и его приложения 2021 Т. 55 № 4 С. 22-39
In a recent paper, given an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of local functionals, which conjecturally gives a second Hamiltonian structure for the double ramification hierarchy associated to the CohFT. In this paper we prove this conjecture in ...
Added: September 14, 2022
Buryak A., Gubarevich D., Mathematical Physics Analysis and Geometry 2023 Vol. 26 No. 3 Article 23
One of many manifestations of a deep relation between the topology of the moduli spaces of algebraic curves and the theory of integrable systems is a recent construction of Arsie, Lorenzoni, Rossi, and the first author associating an integrable system of evolutionary PDEs to an F-cohomological field theory (F-CohFT), which is a collection of cohomology ...
Added: November 20, 2023
Buryak A., Netser Zernik A., Pandharipande R. et al., Advances in Mathematics 2022 Vol. 401 Article 108249
We define stationary descendent integrals on the moduli space of stable maps from disks to (CP^1,RP^1). We prove a localization formula for the stationary theory involving contributions from the fixed points and from all the corner-strata. We use the localization formula to prove a recursion relation and a closed formula for all genus 0 disk cover ...
Added: September 14, 2022
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
Buryak A., Rossi P., Bulletin of the London Mathematical Society 2021 Vol. 53 No. 3 P. 843-854
In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the ...
Added: February 1, 2021
Buryak A., Clader E., Tessler R., Journal of Geometry and Physics 2023 Vol. 192 Article 104960
In our previous two papers, we constructed an r-spin theory in genus zero for Riemann surfaces with boundary and fully determined the corresponding intersection numbers, providing an analogue of Witten's r-spin conjecture in genus zero in the open setting. In particular, we proved that the generating series of open r-spin intersection numbers is determined by the genus-zero part ...
Added: November 20, 2023
Bruzzo U., Markushevich D., Tikhomirov A. S., European Journal of Mathematics 2016 Vol. 2 P. 73-86
We study the moduli space $I_{n,r}$In,r of rank-2r symplectic instanton vector bundles on $\mathbb{P}^3$ℙ3 with $r\ge 2$r⩾2 and second Chern class $n\ge r+1, n-r\equiv 1(\mathrm{mod} 2)$n⩾r+1,n−r≡1(mod2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I_{n,r}^*$I∗n,r of tame symplectic instantons is irreducible and has the expected dimension equal to ...
Added: December 28, 2015
Polishchuk A., Lekili Y., Journal fuer die reine und angewandte Mathematik 2019 Vol. 2019 No. 755 P. 151-189
We show that a certain moduli space of minimal A∞-structures coincides with the modular compactification ℳ_{1,n}(n−1)of ℳ_{1,n} constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational ...
Added: May 10, 2020
Gorsky E., Mathematical Research Letters 2009 Vol. 16 No. 4 P. 591-603
The generating function for Sn-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g ≥ 2 is calculated. This answer generalizes the known ones for genera 2 and 3 and the answers obtained by J. Bergstro ̈m for any genus and n ≤ 7 points. ...
Added: December 9, 2014
Kochetkov Y., / Cornell University Library. 2013. No. 1301.6059.
We consider the space $\mathcal{M}_{2,1}$ --- the open moduli space of complex curves of genus 2 with one marked point. Using language of chord diagrams we describe the cell structure of $\mathcal{M}_{2,1}$ and cell adjacency. This allows one to construct matrices of boundary operators and compute Betty numbers of $\mathcal{M}_{2,1}$ over $\mathbb{Q}$. ...
Added: February 24, 2013
Прасолов В. В., Schwarzman O., МЦНМО, 2014
Книга, адресованная студентам физико-математических специальностей написана на основе лекций, прочитанных авторами в Независимом
московском университете.
В первой части изложены основы теории алгебраических кривых, рассматриваемых как римановы поверхности. Здесь преобладают сравнительно элементарные алгебраические и геометрические методы. Новинкой для
учебной литературы такого уровня является обсуждение связи алгебраических кривых с теорией Галуа. Впервые на русском языке изложены теоремы
Ритта о композициях многочленов ...
Added: March 18, 2015
Lopatkin V., Nam T. G., Journal of Algebra 2017 No. 481 P. 273-292
In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra LK(E) of a finite graph E with coefficients in a commutative ring K, as well as establish a formula for calculating the homological dimensions of LK(E) when K is a commutative unital algebra over a field. ...
Added: October 29, 2021
Brauer Gomez O., Buryak A., Journal of High Energy Physics 2021 Vol. 2021 P. 1-15
The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation ...
Added: February 1, 2021
Модули математических инстантонных векторных расслоений с нечетным $c_2$ на проективном пространстве
Tikhomirov A. S., Известия РАН. Серия математическая 2012 Т. 76 № 5 С. 143-224
Изучается пространство $I_n$ модулей математических инстантонных векторных расслоений ранга 2 со вторым классом Черна $n\ge1$ на проективном пространстве $\mathbb{P}^3$. Доказывается неприводимость $I_n$ для произвольного нечетного $n\ge1$. Ключевые слова: векторные расслоения, математические инстантоны, пространство модулей. Адрес сайта: http://www.mathnet.ru/php/archive.phtmlwshow=paper&jrnid=im&paperid=4134&option_lang=rusм ...
Added: October 21, 2014
Tikhomirov A. S., Известия РАН. Серия математическая 2013 Т. 77 № 6 С. 139-167
Исследуется проблема неприводимости пространства модулей $I_n$ инстантонных векторных расслоений ранга 2 со вторым классом Черна $n\ge1$ на проективном пространстве $\mathbb{P}^3$ (неприводимость $I_n$ для нечетных значений $n$ была доказана автором в 2012 г.). Доказана неприводимость проcтранства $I_n$ для произвольного четного значения $n\ge2$, что влечет неприводимость $I_n$ для всех $n\ge1$. ...
Added: October 21, 2014
Tikhomirov A. S., Заводчиков М. А., Моделирование и анализ информационных систем 2014 Т. 21 № 2 С. 90-96
В статье доказывается приводимость пространства $M_{\mathbb{P}^3}^{\rm ref}$ модулей стабильных рефлексивных пучков ранга 2 с классами Черна $c_1=-1,\ c_2=4,\ c_3=2$ на $\mathbb{P}^3$. Это первый пример приводимого пространства в серии пространств модулей стабильных рефлексивных пучков ранга 2 с классами Черна $c_1=-1,\ c_2=4,\ c_3=2m,\ m=1,2,3,4,5,6,8$. Найдены две неприводимые компоненты этого пространства, имеющие ожидаемую размерность 27, и дается их ...
Added: October 20, 2014