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Hodge polynomials of the moduli spaces of rank 3 pairs

Muñoz, Vicente (2008) Hodge polynomials of the moduli spaces of rank 3 pairs. Geometriae Dedicata, 136 . pp. 17-46. ISSN 0046-5755

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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: E(2) -> E(1). There is a concept of stability for triples which depends on a real parameter sigma. In this paper, we determine the Hodge polynomials of the moduli spaces of sigma-stable triples with rk(E(1)) = 3, rk(E(2)) = 1, using the theory of mixed Hodge structures. This gives in particular the Poincare 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.

Item Type:Article
Uncontrolled Keywords:Moduli space; Complex curve; Stable triple; Hodge polynomial
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:17083

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