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Related papers: Moduli of filtered quiver representations

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When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…

Representation Theory · Mathematics 2025-07-29 Yariana Diaz

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.

Algebraic Geometry · Mathematics 2007-05-23 Markus Reineke

The theory of representations of quivers and of their preprojective algebras are reviewed. In particular, moduli spaces of representations of these algebras, quiver varieties and reflection functor are described. The proof that the…

Mathematical Physics · Physics 2019-02-11 A. Silantyev

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

Representation Theory · Mathematics 2014-07-11 E. Babson , B. Huisgen-Zimmermann , R. Thomas

In this article, we study the smoothness of the moduli space of finite quiver vector bundles over the smooth complex projective curves.

Algebraic Geometry · Mathematics 2025-03-18 Amit Kumar Singh

We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…

Representation Theory · Mathematics 2014-07-11 B. Huisgen-Zimmermann

Let G be a Lie group and Q a quiver with relations. In this paper, we define G-valued representations of Q which directly generalize G-valued representations of finitely generated groups. Although as G-spaces, the G-valued quiver…

Geometric Topology · Mathematics 2013-05-14 Carlos Florentino , Sean Lawton

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…

Algebraic Geometry · Mathematics 2015-11-30 Markus Reineke

Suppose $S$ is a smooth projective surface over an algebraically closed field $k$, $\mathcal{L}=\{L_1,\ldots,L_n\}$ is a full strong exceptional collection of line bundles on $S$. Let $Q$ be the quiver associated to this collection. One…

Algebraic Geometry · Mathematics 2019-05-29 Xuqiang Qin , Shizhuo Zhang

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…

Representation Theory · Mathematics 2007-09-18 Vladimir V. Sergeichuk

In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over…

Representation Theory · Mathematics 2023-08-01 William Crawley-Boevey

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…

Representation Theory · Mathematics 2015-08-18 Thorsten Weist

Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted…

Representation Theory · Mathematics 2018-08-01 Mike Prest

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a…

Representation Theory · Mathematics 2014-02-21 M. Domokos , Dániel Joó

We provide a general method for constructing moduli stacks whose points are diagrams of vector bundles over a fixed base, indexed by a fixed simplicial set -- that is, quiver bundles of a fixed shape. We discuss some constraints on the base…

Algebraic Geometry · Mathematics 2025-02-18 Mahmud Azam , Steven Rayan

Given a sufficiently nice collection of sheaves on an algebraic variety V, Bondal explained how to build a quiver Q along with an ideal of relations in the path algebra of Q such that the derived category of representations of Q subject to…

Algebraic Geometry · Mathematics 2011-08-31 Aaron Bergman , Nicholas J. Proudfoot

We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\times n$ matrices to (block) upper triangular matrices up to…

Algebraic Geometry · Mathematics 2016-07-11 Mee Seong Im

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

Algebraic Geometry · Mathematics 2007-05-23 Arne B. Sletsjoe

We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to selectivity for ultrafilters on the natural…

Logic · Mathematics 2024-07-22 Iian B. Smythe

We compute the Brauer groups of several moduli spaces of stable quiver representations.

Algebraic Geometry · Mathematics 2014-10-03 Markus Reineke , Stefan Schroeer