Search

In this paper, we study triples of the form (E, theta, phi) over a compact Riemann Surface, where (E, theta) is a Higgs bundle and phi is a global holomorphic section of the Higgs bundle. Our main result is a description of a birational equivalence which relates geometrically the moduli space of Higgs bundles of rank r and degree d to the moduli space of Higgs bundles of rank (r-1) and degree d., Comment: 20 pages, same as before, with a correction in the references

We study the moduli space of Higgs bundles on a compact Riemann surface. It was shown by Thaddeus and Hausel (in rank 2) and Markman (in general rank) that the rational cohomology ring of this space is generated by universal classes. In this paper, we use their results to compute the Hodge structure on the cohomology of this moduli space. We show that the natural Hodge structure on H^k is pure of weight k., Comment: 7 pages. The only change is the addition of a reference to the proof of the generation theorem for general rank by E. Markman