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On the S_n-equivariant Euler characteristic of M_{2,n}.
Cornell University
,
2007.
Gorsky E.
The Getzler's formula relates the S_n-equivariant Hodge-Deligne polynomial of the space of ordered tuples of distinct points on a given variety X with the Hodge-Deligne polynomial of X. We obtain the analogue of this formula for the case when X has a nontrivial automorphism group. Collecting together all strata of M_2 with different automorphism groups, we derive a formula for the S_n-equivariant Euler characteristic of M_{2,n}.
2 with different automorphism groups, we derive a formula for the S_n-equivariant Euler characteristic of
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
Gorsky E., Advances in Mathematics 2014 Vol. 250 P. 588-595
We derive a formula for the Sn-equivariant Euler characteristic of the moduli space Mg,n of genus g curves with n marked points. ...
Added: December 9, 2014
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
Basalaev A., Buryak A., Arnold Mathematical Journal 2019 Vol. 5 No. 2-3 P. 145-186
In their fundamental work, Dubrovin and Zhang, generalizing the Virasoro equations for the genus 0 Gromov–Witten invariants, proved the Virasoro equations for a descendent potential in genus 0 of an arbitrary conformal Frobenius manifold. More recently, a remarkable system of partial differential equations, called the open WDVV equations, appeared in the work of Horev and ...
Added: April 21, 2020
Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2016.
Consider the space M = O(p, q)/O(p) × O(q) of positive p-dimensional subspaces in a pseudo-Euclidean space V of signature (p, q), where p > 0, q > 1 and (p, q) != (1, 2), with integral structure: V = VZ ⊗ R. Let Γ be an arithmetic subgroup in G = O(VZ), and R ...
Added: April 14, 2016
Kuznetsov A., Debarre O., / Cornell University. Series arXiv "math". 2018.
We describe the moduli stack of Gushel-Mukai varieties as a global quotient stack and its coarse moduli space as the corresponding GIT quotient. The construction is based on a comprehensive study of the relation between this stack and the stack of Lagrangian data; roughly speaking, we show that the former is a generalized root stack ...
Added: June 8, 2019
Kochetkov Y., / Cornell Univercity. Series arXiv.org e-print archive "arXiv.math". 2022. No. 02069.
A polynomial $p\in \mathbb{C}[z]$ with three finite values is called the Zolotarev polynomial. For a class of such
polynomials with the given degree, given passport and simple critical points we define a \emph{combinatorial moduli space}. A combinatorial moduli space have the same essential properties as analytical moduli space, but much easier to construct. We study these objects for Zolotarev polynomials of ...
Added: November 9, 2022
Ebeling W., Gusein-Zade S., International Mathematics Research Notices 2021 Vol. 2021 No. 16 P. 12305-12329
A.Takahashi suggested a conjectural method to find mirror symmetric pairs consisting of invertible polynomials and symmetry groups generated by some diagonal symmetries and some permutations of variables. Here we generalize the Saito duality between Burnside rings to a case of non-abelian groups and prove a "non-abelian" generalization of the statement about the equivariant Saito duality ...
Added: August 26, 2021
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
Ebeling W., Gusein-Zade S., Pure and Applied Mathematics Quarterly 2020 Vol. 16 No. 4 P. 1099-1113
In the framework of constructing mirror symmetric pairs of Calabi-Yau manifolds, P.Berglund, T.Hubsch and M.Henningson considered a pair (f,G) consisting of an invertible polynomial f and a finite abelian group G of its diagonal symmetries and associated to this pair a dual pair (f~, G~). A.Takahashi suggested a generalization of this construction to pairs (f, ...
Added: February 3, 2021
Amerik E., Verbitsky M., Journal of Geometry and Physics 2015 Vol. 97 P. 44-50
Let S be an infinite-dimensional manifold of all symplectic, or hyperkähler, structures on a compact manifold M, and Diff0 the connected component of its diffeomorphism group. The quotient S/Diff0 is called the Teichmüller space of symplectic (or hyperkähler) structures on M. MBM classes on a hyperkähler manifold M are cohomology classes which can be represented ...
Added: September 8, 2015
Aleksei Ivanov, Tikhomirov A. S., Journal of Geometry and Physics 2018 Vol. 129 P. 90-98
We describe new irreducible components of the Gieseker-Maruyama moduli scheme M(3) of semistable rank 2 coherent sheaves with Chern classes c1=0, c2=3, c3=0 on P^3, general points of which correspond to sheaves whose singular loci contain components of dimensions both 0 and 1. These sheaves are produced by elementary transformations of stable reflexive rank 2 ...
Added: February 25, 2018
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
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
Tikhomirov A. S., Bruzzo U., Markushevich D., Central European Journal of Mathematics 2012 Vol. 10 No. 4 P. 1232-1245
Symplectic instanton vector bundles on the projective space $\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space $I_{n;r}$ of rank-$2r$ symplectic instanton vector bundles on $\mathbb{P}^3$ with $r\ge2$ and second Chern class $n\ge r, n\equiv r(\mod 2)$. We introduce the notion of tame symplectic instantons by excluding a kind ...
Added: October 21, 2014
Moduli of symplectic instanton vector bundles of higher rank on projective space $\mathbb{P^3}$. II.
Tikhomirov A. S., Bruzzo U., Markushevich D., / Max Planck Institute for Mathematics. Series MPIM "MPIM". 2014. No. 2014-22.
Symplectic instanton vector bundles on the projective space $\mathbb{P^3}$ are a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\mathbb{P^3}$ with $r\ge2$ and second Chern class $n\ge r+1,\ n-r \equiv 1(\mod2)$. We introduce the notion of tame symplectic instantons by excluding a ...
Added: October 19, 2014
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
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
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017