23 citations · 33 across the 12 of their papers we have counts for
14 papers
Highest weight categories via pairs of dual exceptional sequences
Agnieszka Bodzenta, Alexey Bondal
In this paper we present criteria in terms of dual pairs of exceptional sequences for an abelian category to be highest weight. The criteria are applied in three situations of geom…
Reconstruction of a surface from the category of reflexive sheaves
Agnieszka Bodzenta, Alexey Bondal
We define a normal surface to be codim-2-saturated if any open embedding of into a normal surface with the complement of codimension 2 is an isomorphism. We show that any n…
Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds
Alexey Bondal, Alexei Rosly
We construct a twist-closed enhancement of the category , the bounded derived category of complexes of -modules with coherent cohomolog…
Abelian envelopes of exact categories and highest weight categories
Agnieszka Bodzenta, Alexey Bondal
We define admissible and weakly admissible subcategories in exact categories and prove that the former induce semi-orthogonal decompositions on the derived categories. We develop t…
Theory of homotopes in application to mutually unbiased bases, harmonic analysis on graphs and perverse sheaves
Alexey Bondal, Ilya Zhdanovskiy
The paper is the survey of the modern results and applications of the theory of homotopes. The notion of a well-tempered element in an associative algebra is introduced and it is p…
Categorifying non-commutative deformations
Agnieszka Bodzenta, Alexey Bondal
We define the functor of non-commutative deformations of an -tuple of objects in an arbitrary -linear abelian category . In o…