scholarly journals Moduli spaces of meromorphic connections and quiver varieties

2014 ◽  
Vol 266 ◽  
pp. 120-151 ◽  
Author(s):  
Kazuki Hiroe ◽  
Daisuke Yamakawa
Keyword(s):  
Moduli Spaces ◽  
Quiver Varieties ◽  
Meromorphic Connections

scholarly journals Quivers and the Euclidean algebra (Extended abstract)

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Alistair Savage
Keyword(s):  
Moduli Spaces ◽  
Euclidean Group ◽  
Quiver Varieties ◽  
Nous Permet ◽  
Preprojective Algebras ◽  
Nous Montrons ◽  
Wild Representation Type ◽  
Il Y A ◽  
International Audience ◽  
Euclidean Algebra

International audience We show that the category of representations of the Euclidean group $E(2)$ is equivalent to the category of representations of the preprojective algebra of the quiver of type $A_{\infty}$. Furthermore, we consider the moduli space of $E(2)$-modules along with a set of generators. We show that these moduli spaces are quiver varieties of the type considered by Nakajima. These identifications allow us to draw on known results about preprojective algebras and quiver varieties to prove various statements about representations of $E(2)$. In particular, we show that $E(2)$ has wild representation type but that if we impose certain combinatorial restrictions on the weight decompositions of a representation, we obtain only a finite number of indecomposable representations. Nous montrons que la catégorie des représentations du groupe d'Euclide $E(2)$ est équivalente à la catégorie des représentations de l'algèbre préprojective de type $A_{\infty}$. De plus, nous considérons l'espace classifiant de modules de $E(2)$ avec un ensemble de générateurs. Nous montrons que ces espaces sont de variétés de carquois de Nakajima. Cette identification nous permet d'utiliser des résultats des algèbres préprojectives et des variétés de carquois pour prouver des affirmations sur des représentations de $E(2)$. En particulier, nous montrons que le type de représentations de $E(2)$ est sauvage mais si nous imposons des restrictions aux poids d'une représentation, il y a seulement un nombre fini de représentations qui ne sont pas décomposables.

scholarly journals Perverse bundles and Calogero–Moser spaces

2008 ◽  
Vol 144 (6) ◽  
pp. 1403-1428 ◽  
Author(s):  
David Ben-Zvi ◽  
Thomas Nevins
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Hilbert Schemes ◽  
Simple Description ◽  
Quiver Varieties ◽  
Complex Curves ◽  
Noncommutative Version ◽  
Cotangent Bundles ◽  
Rank One ◽  
Torsion Free

AbstractWe present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.

Corrigendum and addendum to “Moduli spaces of framed sheaves and quiver varieties”

2017 ◽  
Vol 121 ◽  
pp. 176-179
Author(s):  
Claudio Bartocci ◽  
Valeriano Lanza ◽  
Claudio L.S. Rava
Keyword(s):  
Moduli Spaces ◽  
Quiver Varieties ◽  
Framed Sheaves

scholarly journals LOCAL STRUCTURE OF MODULI SPACES

2011 ◽  
Vol 22 (12) ◽  
pp. 1683-1709
Author(s):  
FRANCOIS-XAVIER MACHU
Keyword(s):  
Automorphism Group ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Local Structure ◽  
Slice Theorem ◽  
Meromorphic Connections

We provide a sketch of the GIT construction of the moduli spaces for the three classes of connections: the class of meromorphic connections with fixed divisor of poles D and its subclasses of integrable and integrable logarithmic connections. We use the Luna Slice Theorem to represent the germ of the moduli space as the quotient of the Kuranishi space by the automorphism group of the central fiber. This method is used to determine the singularities of the moduli space of connections in some examples.

Quasimaps to Zero-Dimensional A∞-Quiver Varieties

2020 ◽  
Author(s):  
Hunter Dinkins ◽  
Andrey Smirnov
Keyword(s):  
Euler Characteristic ◽  
Moduli Spaces ◽  
Combinatorial Formula ◽  
Quiver Varieties ◽  
Symplectic Duality

Abstract We consider the moduli spaces of quasimaps to zero-dimensional $A_{\infty }$ Nakajima quiver varieties. An explicit combinatorial formula for the equivariant Euler characteristic of these moduli spaces is obtained and applications to symplectic duality are discussed.

scholarly journals Group actions on quiver varieties and applications

2019 ◽  
Vol 30 (02) ◽  
pp. 1950007 ◽  
Author(s):  
Victoria Hoskins ◽  
Florent Schaffhauser
Keyword(s):  
Finite Groups ◽  
Moduli Spaces ◽  
Group Actions ◽  
Group Cohomology ◽  
Quiver Representations ◽  
Quiver Varieties ◽  
Algebraic Actions

We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a modular interpretation of each component. As an application, we construct branes in hyperkähler quiver varieties, as fixed loci of such actions.

scholarly journals On the equations and classification of toric quiver varieties

2016 ◽  
Vol 146 (2) ◽  
pp. 265-295 ◽  
Author(s):  
Mátyás Domokos ◽  
Dániel Joó
Keyword(s):  
Projective Space ◽  
Moduli Spaces ◽  
Toric Variety ◽  
Projective Variety ◽  
Homogeneous Ideal ◽  
Quiver Representations ◽  
Canonical Embedding ◽  
Quiver Varieties ◽  
Fixed Dimension

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight, there is an associated quasi-projective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with no oriented cycles the homogeneous ideal of this embedded projective variety is generated by elements of degree at most 3. In each fixed dimension d up to isomorphism there are only finitely many d-dimensional toric quiver varieties. A procedure for their classification is outlined.

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