9 papers
Cluster scattering diagrams via quiver moduli and tight gradings
Amanda Burcroff, Kyungyong Lee, Lang Mou +2
We study rank-2 cluster scattering diagrams through moduli spaces of quiver representations and a recently developed combinatorial framework of tight gradings. Combining quiver-the…
Punctual noncommutative Hilbert schemes
Markus Reineke
Punctual noncommutative Hilbert schemes are projective varieties parametrizing finite codimensional left ideals in noncommutative formal power series rings. We determine their moti…
Counting generating spaces of matrices
Markus Reineke
We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counti…
Spherical representation spaces of quivers
Jennifer Müller, Markus Reineke
We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.
Local intersection cohomology of varieties of complexes
Xin Fang, Markus Reineke
We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit construct…
Motives of Nullcones of Quiver Representations
Lydia Gösmann, Markus Reineke
We derive two formulas for motives of nullcones of quiver representations, one being explicit, the other being of wall-crossing type.
Expander representations of quivers
Markus Reineke
We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove exist…
Motives of central slope Kronecker moduli
Alexandre Astruc, Frederic Chapoton, Karen Martinez +1
We use dualities of quiver moduli induced by reflection functors to describe generating series of motives of Kronecker moduli spaces of central slope as solutions of algebraic and…
Donaldson-Thomas invariants of symmetric quivers
Markus Reineke
We review several algebraic, combinatorial and geometric interpretations of motivic Donaldson-Thomas invariants of symmetric quivers.