Abelian quiver invariants and marginal wall-crossing

Abstract

We prove the equivalence of (a slightly modified version of) the wall-crossing formula of Manschot, Pioline and Sen and the wall-crossing formula of Kontsevich and Soibelman. The former involves abelian analogues of the motivic Donaldson-Thomas type invariants of quivers with stability introduced by Kontsevich and Soibelman, for which we derive positivity and geometricity properties.

24 pages

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Wall-Crossing from Boltzmann Black Hole Halos
• From Black Holes to Quivers
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants

Cited by in corpus (5)

• On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants
• Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
• The Coulomb Branch Formula for Quiver Moduli Spaces
• Block-Göttsche invariants from wall-crossing
• Quiver indices and Abelianization from Jeffrey-Kirwan residues