Geometriae Dedicata

, Volume 136, Issue 1, pp 17–46 | Cite as

Hodge polynomials of the moduli spaces of rank 3 pairs

  • Vicente MuñozEmail author
Original Paper


Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple \({(E_1, E_2, \phi)}\) on X consists of two holomorphic vector bundles E 1 and E 2 over X and a holomorphic map \({\phi \colon E_{2}\to E_{1}}\) . There is a concept of stability for triples which depends on a real parameter σ. In this paper, we determine the Hodge polynomials of the moduli spaces of σ-stable triples with rk(E 1) = 3, rk(E 2) = 1, using the theory of mixed Hodge structures. This gives in particular the Poincaré polynomials of these moduli spaces. As a byproduct, we recover the Hodge polynomial of the moduli space of odd degree rank 3 stable vector bundles.


Moduli space Complex curve Stable triple Hodge polynomial 

Mathematics Subject Classification (2000)

14F45 14D20 14H60 


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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UC3MConsejo Superior de Investigaciones CientíficasMadridSpain

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