Abstract
Motivated by string-theoretic arguments Manschot, Pioline and Sen discovered a new remarkable formula for the Poincaré polynomial of a smooth compact moduli space of stable quiver representations which effectively reduces to the abelian case (ie 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.
Citation
Markus Reineke. Jacopo Stoppa. Thorsten Weist. "MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence." Geom. Topol. 16 (4) 2097 - 2134, 2012. https://doi.org/10.2140/gt.2012.16.2097
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