2 citations · 6 across the 8 of their papers we have counts for
9 papers
Root stacks and periodic decompositions
Agnieszka Bodzenta, Will Donovan
For an effective Cartier divisor D on a scheme X we may form an nth root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and…
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…
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…
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…
Canonical tilting relative generators
Agnieszka Bodzenta, Alexey Bondal
Given a relatively projective birational morphism of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over ) genera…
Ringel duality as an instance of Koszul duality
Agnieszka Bodzenta, Julian Külshammer
In their previous work, S. Koenig, S. Ovsienko and the second author showed that every quasi-hereditary algebra is Morita equivalent to the right algebra, i.e. the opposite algebra…
Flops and spherical functors
Agnieszka Bodzenta, Alexey Bondal
We study derived categories of Gorenstein varieties X and X^+ connected by a flop. We assume that the flopping contractions f: X \to Y, f^+: X^+ \to Y have fibers of dimension boun…
DG quivers of smooth rational surfaces
Agnieszka Bodzenta
Let X be a smooth rational surface. We calculate a DG quiver of a full exceptional collection of line bundles on X obtained by an augmentation from a strong exceptional collection…
DG categories and exceptional collections
Agnieszka Bodzenta
Bondal and Kapranov describe how to assign to a full exceptional collection on a variety X a DG category C such that the bounded derived category of coherent sheaves on X is equiva…