We present an algorithm that finds all toric noncommutative crepant resolutions of a given
toric 3-dimensional Gorenstein singularity. The algorithm embeds the quivers of these …

We investigate full strongly exceptional collections on smooth, complete toric varieties. We
obtain explicit results for a large family of varieties with Picard number three, containing …

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line
bundles on rational C^*-surfaces under homogeneous degenerations. In particular, we …

Let X be a toric Fano manifold and denote by C rit (f X)⊂(C∗) n the solution scheme of the
corresponding Landau–Ginzburg system of equations. For toric Del-Pezzo surfaces and …

A description of how to assign to a full exceptional collection on a variety $ X $ a DG
category $\mathcal {C} $ such that the bounded derived category of coherent sheaves on …

We prove the existence of tilting objects on generalized Brauer--Severi varieties, some
relative flags and some twisted forms of relative flags. As an application we obtain tilting …

In their paper [Exceptional sequences of invertible sheaves on rational surfaces, Compositio
Math. 147 (2011), 1230–1280], Hille and Perling associate to every cyclic full strongly …

We show how one-parameter homogeneous deformations of rational T-varieties induce
maps from a subgroup of the Picard group of any fiber of the deformation to the Picard group …

We classify Fano polygons with finite mutation class. This classification exploits a
correspondence between Fano polygons and cluster algebras, refining the notion of …

Let X be a toric Fano manifold given by a reflexive polytope Δ and let C rit (f)⊂(C*) s be the
solution scheme of the Landau–Ginzburg system associated with a Laurent polynomial fu …