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Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants

Part of: Representation theory of rings and algebras Families, fibrations

Published online by Cambridge University Press:  15 February 2011

Markus Reineke
Markus Reineke*
Affiliation:
Fachbereich C – Mathematik, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany (email: reineke@math.uni-wuppertal.de)
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Abstract

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A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert-scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson–Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.

Keywords

quiver modulifunctional equationswall crossingDonaldson–Thomas invariants

MSC classification

Secondary: 16G20: Representations of quivers and partially ordered sets 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 3 , May 2011 , pp. 943 - 964
Copyright
Copyright © Foundation Compositio Mathematica 2011

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