HODGE POLYNOMIALS OF THE MODULI SPACES OF TRIPLES OF RANK (2,2)

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)) = rk(E(2)) = 2, using the theory of mixed Hodge structures (in the cases that these moduli spaces are smooth and compact). This gives in particular the Poincare polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.