Moduli of representations of quivers

Abstract

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 motivated, and the construction of moduli spaces is reviewed. Topological, arithmetic and algebraic methods for the study of moduli spaces are discussed.

Overview paper for the Proceedings of the ICRA XII conference, Torun, 2007; 50 pages

References in corpus (7)

• Four Dimensional Black Hole Microstates: From D-branes to Spacetime Foam
• Lectures on Noncommutative Geometry
• Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
• Cohomology of non-commutative Hilbert schemes
• The projective invariants of ordered points on the line
• Smooth models of quiver moduli
• On the number of stable quiver representations over finite fields

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• On the Harder-Narasimhan filtration for finite dimensional representations of quivers
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• A Gaussian distribution for refined DT invariants and 3D partitions
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• Tree normal forms for quiver representations
• Counting Semistable Representations of Quivers over Finite Fields
• Holomorphic aspects of moduli of representations of quivers
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