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

2011/02/15 by Markus Reineke · 10 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory

paper · pdf · doi:10.1112/s0010437x1000521x

Abstract

Abstract 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.

Cited by

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• A refinement of the A-polynomial of quivers
• Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Donaldson-Thomas theory for categories of homological dimension one with potential
• Computations in equivariant Gromov-Witten theory of GKM spaces
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