Hodge polynomials of the moduli spaces of pairs.

Abstract

Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic pair on X is a couple (E,ϕ), where E is a holomorphic bundle over X of rank n and degree d, and ϕ ∈ H0(E) is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which E has fixed determinant.