Hodge polynomials of the moduli spaces of pairs

Abstract

Let $X$ be a smooth projective curve of genus $g\ge 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\varphi )$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\varphi \in H^0(E)$ 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 changes

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