### ?

## Coherent Sheaves, Chern Classes, and Superconnections on compact complex-analytic manifolds

Izvestiya. Mathematics. 2022.

Bondal A. I., Rosly A. A.

We construct a twist-closed enhancement of the category Dbcoh(X), the bounded derived category of complexes of OX-modules with coherent cohomology, by means of the DG-category of ∂¯-superconnections. Then we apply the techniques of ∂¯-superconnections to dene Chern classes and Bott–Chern classes of objects in the category, in particular, of coherent sheaves.

Bondal Alexey, Rosly Alexei, Derived categories for complex-analytic manifolds / . 2011.

We construct a twist-closed enhancement of the derived category of coherent sheaves on a smooth compact complex-analytic manifold by means of DG-category of dbar-superconnections. ...

Added: October 30, 2013

Alexey Bondal, Kavli Institute for the Physics and Mathematics of the Universe News 2011 Vol. 14 P. 4-9

Дается взгляд на развитие идей гомологической алгебры и их приложений к алгебраической геометрии. Описывается связь с зеркальной симметрией и предлагается гомотопическая интерпретация категории производных категорий. ...

Added: October 14, 2013

Fonarev A., Transformation Groups 2020

We construct a minimal Lefschetz decomposition of the bounded derived category of coherent sheaves on the isotropic Grassmannian IGr(3, 7). Moreover, we show that IGr(3, 7) admits a full exceptional collection consisting of equivariant vector bundles. ...

Added: September 27, 2021

Piontkovski D., Noncommutative Grassmannian of codimension two has coherent coordinate ring / Cornell University. Series math "arxiv.org". 2014. No. arXiv:1401.6549.

A noncommutative Grassmanian NGr(m,n) is introduced by Efimov, Luntz, and Orlov in `Deformation theory of objects in homotopy and derived categories III: Abelian categories' as a noncommutative algebra associated to an exceptional collection of n-m+1 coherent sheaves on P^n. It is a graded Calabi--Yau Z-algebra of dimension n-m+1. We show that this algebra is coherent ...

Added: May 13, 2014

Antipov M., Zvonareva A., Mathematische Zeitschrift 2022 Vol. 301 No. 2 P. 1963-1981

In this paper the class of Brauer graph algebras is proved to be closed
under derived equivalence. For that we use the rank of the maximal torus of the identity
component of the group of outer automorphisms Out0(A) of a symmetric stably biserial
algebra A. ...

Added: November 1, 2019

Bergh D., Gorchinskiy S., Lunts V. et al., Journal of Algebraic Geometry 2021 Vol. 30 P. 685-757

Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases that these two measures coincide. This implies, in particular, ...

Added: November 17, 2021

Bondal A. I., Bodzenta-Skibinska A., Advances in Mathematics 2018 Vol. 323 P. 226-278

Given a relatively projective birational morphism f : X → Y
of smooth algebraic spaces with dimension of fibers bounded
by 1, we construct tilting relative (over Y) generators TX,f
and S_X,f in D^b(X). We develop a piece of general theory of
strict admissible lattice filtrations in triangulated categories
and show that D^b(X) has such a filtration L where the ...

Added: May 2, 2018

Guseva L., On the derived category of IGr(3,8) / Cornell University. Series math "arxiv.org". 2018.

We construct a full exceptional collection of vector bundles in the bounded derived category of
coherent sheaves on the Grassmannian IGr(3,8) of isotropic 3-dimensional subspaces in a symplectic vector
space of dimension 8. ...

Added: October 19, 2018

Zürich : European Mathematical Society Publishing house, 2012

The study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics. The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic ...

Added: October 14, 2013

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

Elagin A. D., Lunts V., Schnürer O., Moscow Mathematical Journal 2020 Vol. 20 No. 2 P. 277-309

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, thereby answering a question of Iyama. More generally, we prove this statement for any algebra over a perfect field that is finite over its center and whose center is finitely generated ...

Added: May 11, 2020

Antipov M., Звонарёва А. О., Journal of Mathematical Sciences 2014 Vol. 202 No. 3 P. 333-345

In this paper, all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 are described, using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an application, all two-term tilting complexes over a Brauer star algebra are described and their endomorphism rings are ...

Added: December 25, 2018

Finkelberg M. V., Braverman A., A quasi-coherent description of the the category of D-mod(Gr_GL(n)) / Cornell University. Series arXiv "math". 2018.

In arXiv:1807.09038 we formulated a conjecture describing the derived category D-mod(Gr_GL(n)) of (all) D-modules on the affine Grassmannian of the group GL(n) as the category of ind-coherent sheaves on a certain stack (it is explained in loc. cit. that this conjecture "follows" naturally from some heuristic arguments involving 3-dimensional quantum field theory). In this paper we prove a ...

Added: December 3, 2018

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

Kuznetsov A., International Mathematics Research Notices 2021 Vol. 2021 No. 12 P. 9262-9339

We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a ...

Added: December 12, 2022

Piontkovski D., Journal of Noncommutative Geometry 2016

A noncommutative Grassmanian NGr(m,n) is introduced by Efimov, Luntz, and Orlov in `Deformation theory of objects in homotopy and derived categories III: Abelian categories' as a noncommutative algebra associated to an exceptional collection of n-m+1 coherent sheaves on P^n. It is a graded Calabi--Yau Z-algebra of dimension n-m+1. We show that this algebra is coherent ...

Added: April 14, 2016

Elagin Alexey, Lunts Valery, Schnürer O., Smoothness of Derived Categories of Algebras / Cornell University. Series arXiv "math". 2018.

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for any algebra over a perfect field that is finite over its center and whose center is finitely generated ...

Added: December 1, 2018

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016

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

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

Buchstaber V., Limonchenko I., Embeddings of moment-angle manifolds and sequences of Massey products / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 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