We characterise subcategories of semistable modules for noncommutative minimal models
of compound Du Val singularities, including the non-isolated case. We find that the stability …

This is an expository survey article on compound Du Val (cDV) singularities, with emphasis
on recent homological approaches, including: noncommutative resolutions, tilting theory …

The first part of this memoir assigns hyperplane arrangements to any choice of vertices in a
Coxeter graph, by taking an intersection arrangement inside a Tits cone. For each such …

We first generalize classical Auslander–Reiten duality for isolated singularities to cover
singularities with a one-dimensional singular locus. We then define the notion of CT …

We first generalize classical Auslander–Reiten duality for isolated singularities to cover
singularities with a one-dimensional singular locus. We then define the notion of CT …

Let X be a singular affine normal variety with coordinate ring R and assume that there is an
R-order admitting a stability structure such that the scheme of relevant semistable …

Given a quiver algebra A with relations defined by a superpotential, this paper defines a set
of invariants of A counting framed cyclic A–modules, analogous to rank–1 Donaldson …

Crepant resolutions of three-dimensional toric Gorenstein singularities are derived
equivalent to noncommutative algebras arising from consistent dimer models. By choosing a …

Associated to each finite subgroup Γ of \ttSL_2(C) there is a family of noncommutative
algebras O^τ(Γ), which is a deformation of the coordinate ring of the Kleinian singularity …

We study infinite dimensional tilting modules over a concealed canonical algebra of
domestic or tubular type. In the domestic case, such tilting modules are constructed by using …