Related papers: Motives of Nullcones of Quiver Representations
We prove wall-crossing formulas for the motivic invariants of the moduli spaces of framed objects in the ind-constructible abelian categories. Developed techniques are applied in the case of the motivic Donaldson-Thomas invariants of…
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 q-difference equations.
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…
We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.
We define and compare two different definitions of Chow motives for Deligne-Mumford stacks, associated with two definitions of Chow rings. The main result we prove is that both categories of motives are equivalent to the usual category of…
We investigate the wall-crossing phenomena for moduli of framed quiver representations. These spaces are expected to be highly useful in capturing the representation theoretic essence of special functions in integrable systems. Within this…
We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.
We provide a decomposition of the equivariant Milnor-Witt motives for the moduli spaces of stable curves $\overline{\mathcal{M}}_{1,2}$.
We explain the role of the boundary motive in the construction of certain Chow motives, and of extensions of Chow motives. Our two main examples concern proper, singular surfaces and fibre products of a universal elliptic curve.
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get…
It is well-known that a quiver Q of type A_n is representation-finite, and that its indecomposable representations are thin (all Jordan-Hoelder multiplicities are 0 or 1). By now, various methods of proof are known. The aim of this note is…
The classical construction of representations of quivers enables us to consider linear maps between several vector spaces. The mixed representations of quivers helps us to work with linear maps as well as bilinear forms on several vector…
We prove that the transcendental motive of any quasi elliptic surface is trivial. To prove this, we focus on the uniruledness of quasi elliptic surfaces.
We study motivic Donaldson-Thomas invariants in the sense of Behrend-Bryan-Szendroi. A wall-crossing formula under a mutation is proved for a certain class of quivers with potentials.
We have two parallel goals of this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the…
Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneous varieties has begun to emerge. In particular,…
Let $n \geq 2$. We introduce the notion of $n$-representations of quivers, and we explicitly provide concrete examples of $2$-representations of quivers. We establish the categories of $n$-representations and investigate kernels and…