Related papers: Local quivers and stable representations

In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered representations uses the…

Torus fixed points of quiver moduli spaces are given by stable representations of the universal (abelian) covering quiver. As far as the Kronecker quiver is concerned they can be described by stable representations of certain bipartite…

We compute rational equivariant Chow rings with respect to a torus of quiver moduli spaces. We derive a presentation in terms of generators and relations, use torus localization to identify it as a subring of the Chow ring of the fixed…

The fixed point set under a natural torus action on projectivized moduli spaces of simple representations of quivers is described. As an application, the Euler characteristic of these moduli is computed.

The purpose of this paper is to describe a method for computing homotopy groups of the space of $\alpha$-stable representations of a quiver with fixed dimension vector and stability parameter $\alpha$. The main result is that the homotopy…

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 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…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…

We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified…

We construct the moduli space of finite dimensional representations of generalized quivers for arbitrary connected complex reductive groups using Geometric Invariant Theory as well as Symplectic reduction methods. We explicit characterize…

This article is based on my lecture notes from summer schools at the Universities of Utah (June 2007) and Warwick (September 2007). We provide an introduction to explicit methods in the study of moduli spaces of quiver representations and…

We construct new moduli spaces of quiver representations with multiplicities, i.e. over rings of truncated power series. This includes moduli of framed representations and analogues of Nakajima quiver varieties. Our construction relies on…

In this paper we introduce several computational techniques for the study of moduli spaces of McKay quiver representations, making use of Groebner bases and toric geometry. For a finite abelian group G in GL(n,k), let Y_\theta be the…

We describe the torus fixed locus of the moduli space of stable sheaves with Hilbert polynomial $4m+1$ on the projective plane. We determine the torus representation of the tangent spaces at the fixed points, which leads to the computation…

We construct small desingularizations of moduli spaces of semistable quiver representations for indivisible dimension vectors using deformations of stabilites and a dimension estimate for nullcones. We apply this construction to several…

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…

We study torus actions on moduli spaces of quivers. First we give a description of the weight spaces of the induced action of the tangent space to a torus-fixed point. Then we focus on actions of tori of rank one and derive an explicit form…

We analyze the local structure of the moduli space of semi-stable bundles on a curve. In particular, a complete description of the local structure is given in the rank 2 case. We obtain as a corollary of this analysis new results about the…

We study the local structure of the representation variety of a knot group into SL(n,C) at certain diagonal representations. In particular we determine the tangent cone of the representation variety at these diagonal representations, and…

We study the stabilization behavior of cohomology groups associated with moduli spaces of quiver representations for a fixed quiver $Q$. Under mild conditions on a dimension vector $\delta$, we show that the dimensions of these cohomology…