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

Abstract

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. Finally we combine the MPS formula with localization techniques, obtaining a new formula for quiver Euler characteristics as a sum over trees, and constructing many examples of explicit correspondences between quiver representations and tropical curves.

31 pages

References in corpus (1)

• Wall-Crossing from Boltzmann Black Hole Halos

Cited by in corpus (7)

• The quantum tropical vertex
• The Coulomb Branch Formula for Quiver Moduli Spaces
• Block-Göttsche invariants from wall-crossing
• A proof of N.Takahashi's conjecture for $({\mathbb{P}}^2,E)$ and a refined sheaves/Gromov-Witten correspondence
• Quiver indices and Abelianization from Jeffrey-Kirwan residues
• Chow Rings of Fine Quiver Moduli are Tautologically Presented
• Quivers and curves in higher dimension