### ?

## Symplectic instanton bundles on ℙ3 and ’t Hooft instantons

European Journal of Mathematics. 2016. Vol. 2. P. 73-86.

We study the moduli space $I_{n,r}$In,r of rank-2*r* 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 $4n(r+1)-r(2r+1)$.4n(r+1)−r(2r+1) The proof is inherently based on a relation between the spaces $I_{n,r}^*$I∗n,r and the moduli spaces of ’t Hooft instantons.

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

Tikhomirov A. S., Markushevich D., Trautmann G., Central European Journal of Mathematics 2012 Vol. 19 No. 4 P. 1331-1355

We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundled connections an in differential geometry. The new moduli spaces are algebraic spaces arising as quotients ...

Added: October 21, 2014

Jardim M., Markushevich D., Tikhomirov A. S., Moscow Mathematical Journal 2018 Vol. 18 No. 1 P. 117-148

Abstract. Let I(n) denote the moduli space of rank 2 instanton bundles of charge n on P3 . It is known that I(n) is an irreducible, nonsingular and affine variety of dimension 8n − 3. Since every rank 2 instanton bundle on P3 is stable, we may regard I(n) as an open subset of the ...

Added: August 20, 2018

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

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

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

Bogomolov F. A., Lukzen E., / Cornell University. Series arXiv "math". 2020.

We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable ...

Added: October 27, 2020

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

Karasev M., Novikova E., Vybornyi E., Mathematical notes 2017 Vol. 102 No. 5-6 P. 776-786

In the model of Penning trap with a geometric asymmetry we study a resonance regime which produces a hyperbolic type algebra of integrals of motion. The algebra has qubic (non-Lie) commutation relations with creation-anihilation structure. The anharmonic part of the trap potential determines a top-like Hamiltonian over this algebra. The symmetry breaking term generates a ...

Added: October 20, 2017

Tikhomirov A. S., Markushevich D., Verbitsky M., Central European Journal of Mathematics 2012 Vol. 10 No. 4 P. 1185-1187

In this preface we give a short description of the current issue of the Central European Journal of Mathematics containing 22 papers which spin around the topics of the conference “Instantons in complex geometry”, held on March 14–18, 2011 in Moscow. The main goal of the conference was to bring together specialists in complex algebraic ...

Added: October 21, 2014

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

Tikhomirov A. S., Tikhomirov S. A., Васильев Д. А., Siberian Mathematical Journal 2019 Vol. 60 No. 2 P. 343-358

In this article we study the Gieseker–Maruyama moduli spaces B(e, n) of stable rank 2 algebraic vector bundles with Chern classes c1 = e ∈ {−1, 0} and c2 = n ≥ 1 on the projective space P3 . We construct the two new inﬁnite series Σ0 and Σ1 of irreducible components of the spaces ...

Added: August 20, 2019

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

Tikhomirov A. S., Bruzzo U., Markushevich D., Mathematische Zeitschrift 2013 Vol. 275 No. 3-4 P. 1073-1093

We construct a compactification $M^{μss}$ of the Uhlenbeck–Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma: M^{ss}\to M^{μss}$, where $M^{μss}$ is the moduli space of $S$-equivalence classes of Gieseker-semistable framed sheaves. ...

Added: October 20, 2014

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

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

Musaev E., Haupt A., Lechtenfeld O., Journal of High Energy Physics 2014 Vol. 2014 No. 11

Abstract: We consider (1+3)-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kaehler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [1]. We include first order alpha' corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present ...

Added: December 8, 2014

Jardim M., Markushevich D., Tikhomirov A. S., Annali di Matematica Pura ed Applicata 2017 Vol. 196 No. 4 P. 1573-1608

We describe new components of the Gieseker–Maruyama moduli scheme (Formula presented.) of semistable rank 2 sheaves E on (Formula presented.) with (Formula presented.), (Formula presented.) and (Formula presented.) whose generic point corresponds to nonlocally free sheaves. We show that such components grow in number as n grows, and discuss how they intersect the instanton component. ...

Added: February 18, 2017

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

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Borzykh D., ЛЕНАНД, 2021

Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...

Added: February 20, 2021

В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80

Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...

Added: May 3, 2017

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013

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