102 citations · 388 across the 40 of their papers we have counts for
50 papers
Groups generated by spherical twists on K3 surfaces and full exceptional collections on Fano threefolds
Anya Nordskova, Michel Van den Bergh
Let Y be a smooth K3 surface of Picard rank 1. We prove that the subgroup G of Aut D^b(Y) generated by spherical twists with respect to all spherical objects is free. Moreover, we…
HMS symmetries of toric boundary divisors
Špela Špenko, Michel Van den Bergh
Let be a projective crepant resolution of a Gorenstein affine toric variety and let be the LG-model which is the Hori-Vafa mirror dual of . Let …
T-structures on dg-categories and derived deformations
Francesco Genovese, Wendy Lowen, Michel Van den Bergh
This paper is a sequel to "t-structures and twisted complexes on derived injectives" by the same authors. We develop the foundations of the infinitesimal derived deformation theory…
On cohomological and K-theoretical Hall algebras of symmetric quivers
Valery Lunts, Špela Špenko, Michel Van den Bergh
We give a brief review of the cohomological Hall algebra CoHA and the K-theoretical Hall algebra KHA associated to quivers. In the case of symmetric qui…
Catalan numbers, parking functions, permutahedra and noncommutative Hilbert schemes
Valery Lunts, Špela Špenko, Michel Van den Bergh
We find an explicit -equivariant bijection between the integral points in a certain zonotope in , combinatorially equivalent to the permutahedron, and the set of…
Non-commutative crepant resolutions, an overview
Michel Van den Bergh
Non-commutative crepant resolutions (NCCRs) are non-commutative analogues of the usual crepant resolutions that appear in algebraic geometry. In this paper we survey some results a…
On the GKZ discriminant locus
Špela Špenko, Michel Van den Bergh
Let be an integral matrix and let be the convex hull of its columns. By a result of Gelfand, Kapranov and Zelevinski, the so-called principal -determinant locus is equal…
Motivic Atiyah-Segal completion theorem
Gonçalo Tabuada, Michel Van den Bergh
Let T be a torus, X a smooth quasi-compact separated scheme equipped with a T-action, and [X/T] the associated quotient stack. Given any localizing A1-homotopy invariant of dg cate…
Perverse schobers and GKZ systems
Špela Špenko, Michel Van den Bergh
Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy Kähler moduli space (SKMS)…
Freely adjoining monoidal duals
Kevin Coulembier, Ross Street, Michel van den Bergh
Given a monoidal category with an object , we construct a monoidal category by freely adjoining a right dual to . We show tha…
Comparing the Kirwan and noncommutative resolutions of quotient varieties
Špela Špenko, Michel Van den Bergh
Let a reductive group act on a smooth variety such that a good quotient exists. We show that the derived category of a noncommutative crepant resolution (NCCR)…
T-structures and twisted complexes on derived injectives
Francesco Genovese, Wendy Lowen, Michel Van den Bergh
In the paper "Deformation theory of abelian categories", the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitel…
A k-linear triangulated category without a model
Alice Rizzardo, Michel Van den Bergh
In this paper we give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triang…
Non-commutative crepant resolutions for some toric singularities II
Špela Špenko, Michel Van den Bergh
Using the theory of dimer models Broomhead proved that every 3-dimensional Gorenstein affine toric variety Spec R admits a toric non-commutative crepant resolution (NCCR). We give…
A non-commutative Bertini theorem
Jørgen Vold Rennemo, Ed Segal, Michel Van den Bergh
We prove a version of the classical 'generic smoothness' theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a n…
Non-commutative crepant resolutions for some toric singularities I
Špela Špenko, Michel Van den Bergh
We give a criterion for the existence of non-commutative crepant resolutions (NCCR's) for certain toric singularities. In particular we recover Broomhead's result that a 3-dimensio…
A note on non-unique enhancements
Alice Rizzardo, Michel Van den Bergh
We give an easy example of a triangulated category, linear over a field , with two different enhancements, linear over , answering a question of Canonaco and Stellari.
Additive invariants of orbifolds
Goncalo Tabuada, Michel Van den Bergh
In this article, using the recent theory of noncommutative motives, we compute the additive invariants of orbifolds (equipped with a sheaf of Azumaya algebras) using solely "fixed-…
On an analogue of the Markov equation for exceptional collections of length 4
Louis de Thanhoffer de Volcsey, Michel Van den Bergh
We classify the solutions to a system of equations, introduced by Bondal, which encode numerical constraints on full exceptional collections of length 4 on surfaces. The correspond…
Semi-orthogonal decompositions of GIT quotient stacks
Špela Špenko, Michel Van den Bergh
If G is a reductive group which acts on a linearized smooth scheme then we show that under suitable standard conditions the derived category of coherent sheaves of the correspo…
Comparing the commutative and non-commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices
Špela Špenko, Michel Van den Bergh
Let Y be the variety of (skew) symmetric nxn-matrices of rank less than or equal to r. In paper we construct a full faithful embedding between the derived category of a non-commuta…
The Gysin triangle via localization and A1-homotopy invariance
Goncalo Tabuada, Michel Van den Bergh
Let X be a smooth scheme, Z a smooth closed subscheme, and U the open complement. Given any localizing and A1-homotopy invariant of dg categories E, we construct an associated Gysi…
The representation theory of noncommutative
Theo Raedschelders, Michel Van den Bergh
In our companion paper "The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary" we used the Tannaka-Krein formalism to study the universal coacting H…
The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary
Theo Raedschelders, Michel Van den Bergh
For any Koszul Artin-Schelter regular algebra A, we consider a version of the universal Hopf algebra aut(A) coacting on A, introduced by Manin. To study the representations (i.e. f…