Abelian quiver invariants and marginal wall-crossing

TL;DR

This paper establishes the equivalence between two wall-crossing formulas in the context of quiver invariants, providing new insights into motivic Donaldson-Thomas invariants and their properties.

Contribution

It proves the equivalence of two major wall-crossing formulas and derives positivity and geometricity properties for abelian motivic Donaldson-Thomas invariants.

Findings

Proved the equivalence of Manschot-Pioline-Sen and Kontsevich-Soibelman wall-crossing formulas.

Derived positivity properties of abelian motivic Donaldson-Thomas invariants.

Established geometricity properties for these invariants.

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.