Hodge polynomials of the moduli spaces of rank 3 pairs
Tóm tắt
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.
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