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EnglishMotivated 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. [10.2140/gt.2012.16.2097]
| 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 |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| gt-2012-16-045s.pdf | Versione Editoriale (PDF) | Non specificato | Open Access Visualizza/Apri |
http://hdl.handle.net/20.500.11767/17433
