MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence

Understand

Motivated by string-theoretic arguments Manschot, Pioline and Sen discovered a new remarkable formula for the Poincare polynomial of a smooth compact moduli space of stable quiver representations which effectively reduces to the abelian case (i.e.

• thin dimension vectors).
• We first prove a motivic generalization of this formula, valid for arbitrary quivers, dimension vectors and stabilities.
• In the case of complete bipartite quivers we use the refined GW/Kronecker correspondence between Euler characteristics of quiver moduli and Gromov-Witten invariants to identify the MPS formula for Euler characteristics with a standard degeneration formula in Gromov-Witten theory.