Trends in Representation Theory of Algebras and Related Topics


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pp: 589–637

DOI: 10.4171/062-1/14

Moduli of representations of quivers

Markus Reineke[1]

(1) Fachbereich C – Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42097, WUPPERTAL, GERMANY

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.

Keywords: Representations of quiver, invariant theory, moduli space, stability, Betti number, localization, rational point, Hall algebra, Hilbert scheme

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