2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114043Let $X$ be a smooth projective curve of genus $g\geq 2$ 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 $ϕ\in H^0(E)$ 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.23 pages, typos added, minor changesAlgebraic Geometry14F45 (Primary), 14D20, 14H60 (Secondary)text