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. [10.2140/gt.2012.16.2097]

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

Stoppa, Jacopo;
2012

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.
16
4
2097
2134
http://msp.org/gt/2012/16-4/p06.xhtml
Reineke, M.; Stoppa, Jacopo; Thorsten, W.
File in questo prodotto:
File Dimensione Formato  
gt-2012-16-045s.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 388.39 kB
Formato Adobe PDF
388.39 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17433
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 8
social impact