51 citations · 182 across the 12 of their papers we have counts for
15 papers · 1 filter
Derived categories of resolutions of cyclic quotient singularities
Andreas Krug, David Ploog, Pawel Sosna
For a cyclic group acting on a smooth variety with only one character occurring in the -equivariant decomposition of the normal bundle of the fixed point locus, we study…
Some remarks on phantom categories and motives
Pawel Sosna
A phantom category is an admissible subcategory with vanishing Grothendieck group of the bounded derived category of coherent sheaves on a smooth projective variety. The goal of th…
Some properties of dynamical degrees with a view towards cubic fourfolds
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss s…
On the dynamical degrees of reflections on cubic fourfolds
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality proble…
Equivalences of equivariant derived categories
Andreas Krug, Pawel Sosna
We investigate conditions for a Fourier-Mukai transform between derived categories of coherent sheaves on smooth projective stacks endowed with actions by finite groups to lift to…
On the derived category of the Hilbert scheme of points on an Enriques surface
Andreas Krug, Pawel Sosna
We use semi-orthogonal decompositions to construct autoequivalences of Hilbert schemes of points on Enriques surfaces and of Calabi-Yau varieties which cover them. While doing this…
On autoequivalences of some Calabi--Yau and hyperkähler varieties
David Ploog, Pawel Sosna
We show how one can construct new autoequivalences of some Calabi-Yau and hyperk"ahler varieties by passing from a smooth projective surface to the associated Hilbert scheme of poi…
On the Jordan-Hölder property for geometric derived categories
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
We prove that the semiorthogonal decompositions of the derived category of the classical Godeaux surface X do not satisfy the Jordan-Hölder property. More precisely, there are two…
Determinantal Barlow surfaces and phantom categories
Christian Böhning, Hans-Christian Graf von Bothmer, Ludmil Katzarkov +1
We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show t…
On the derived category of the classical Godeaux surface
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5-quotient of the Fermat quintic surface in P^3. This is the maximal possible le…
Scalar extensions of triangulated categories
Pawel Sosna
Given a triangulated category over a field and a field extension , we investigate how one can construct a triangulated category over . Our approach produces the derived…
Linearisations of triangulated categories with respect to finite group actions
Pawel Sosna
Given an action of a finite group on a triangulated category, we investigate under which conditions one can construct a linearised triangulated category using DG-enhancements. In p…
Fourier-Mukai partners of canonical covers of bielliptic and Enriques surfaces
Pawel Sosna
We prove that the canonical cover of an Enriques surface does not admit non-trivial Fourier-Mukai partners. We also show that the canonical cover of a bielliptic surface has at mos…
Stability conditions under change of base field
Pawel Sosna
We investigate the behaviour of Bridgeland stability conditions under change of base field with particular focus on the case of finite Galois extensions. In particular, we prove th…
Derived equivalent conjugate K3 surfaces
Pawel Sosna
We show that there exist a complex projective K3 surface and an automorphism of the complex numbers such that the conjugate K3 surface is a non-isomorphic Fourier-Muk…