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.
MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence / Reineke, M.; Stoppa, Jacopo; Thorsten, W.. - In: GEOMETRY & TOPOLOGY. - ISSN 1465-3060. - 16:4(2012), pp. 2097-2134.
Titolo: | MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence |
Autori: | Reineke, M.; Stoppa, Jacopo; Thorsten, W. |
Rivista: | |
Data di pubblicazione: | 2012 |
Volume: | 16 |
Fascicolo: | 4 |
Pagina iniziale: | 2097 |
Pagina finale: | 2134 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.2140/gt.2012.16.2097 |
URL: | http://msp.org/gt/2012/16-4/p06.xhtml |
Appare nelle tipologie: | 1.1 Journal article |
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