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Moduli spaces of meromorphic connections and quiver varieties  [PDF]
Kazuki Hiroe,Daisuke Yamakawa
Mathematics , 2013,
Abstract: We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties. This result enables us to solve partially the additive irregular Deligne-Simpson problem.
Trace functionals on non-commutative deformations of moduli spaces of flat connections  [PDF]
Philippe Roche,Andras Szenes
Mathematics , 2000,
Abstract: We describe an efficient construction of a canonical non-commutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. We show that this algebra, which is a variant of the quantum moduli algebra introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche, has a trace functional which is related to the canonical trace in the formal index theory of Fedosov and Nest-Tsygan via the Verlinde formula.
Quiver moduli and small desingularizations of some GIT quotients  [PDF]
Markus Reineke
Mathematics , 2015,
Abstract: 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 classes of GIT quotients.
Brauer groups for quiver moduli  [PDF]
Markus Reineke,Stefan Schroeer
Mathematics , 2014,
Abstract: We compute the Brauer groups of several moduli spaces of stable quiver representations.
On singularities of quiver moduli  [PDF]
M. Domokos
Mathematics , 2009,
Abstract: Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected quiver is Dynkin or extended Dynkin if and only if all moduli spaces of its representations are smooth.
Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkahler manifolds, isomonodromic deformations, Painleve equations, and relations to Lie theory  [PDF]
Philip Boalch
Mathematics , 2013,
Abstract: Summary of main work 1999-2012
Poisson automorphisms and quiver moduli  [PDF]
Markus Reineke
Mathematics , 2008,
Abstract: A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing formulas for Donaldson-Thomas type invariants of M. Kontsevich and Y. Soibelman.
Localization in quiver moduli spaces  [PDF]
Thorsten Weist
Mathematics , 2009,
Abstract: 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 quivers coming along with a stable colouring. By use of the glueing method it is possible to construct a huge class of such quivers implying a lower bound for the Euler characteristic. For certain roots it is even possible to construct all torus fixed points.
Quasi-Hamiltonian Geometry of Meromorphic Connections  [PDF]
Philip Boalch
Mathematics , 2002,
Abstract: For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on principal G-bundles over a disc, and they generalise the conjugacy class example of Alekseev, Malkin and Meinrenken (which appears in the simple pole case). Using the `fusion product' in the theory this gives a finite dimensional construction of the natural symplectic structures on the spaces of monodromy/Stokes data of meromorphic connections over arbitrary genus Riemann surfaces, together with a new proof of the symplectic nature of isomonodromic deformations of such connections.
Counting rational points of quiver moduli  [PDF]
Markus Reineke
Mathematics , 2005,
Abstract: It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra of a quiver.
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