We shall dedicate the first half of the talk to introduce classical
Higgs bundles and describe the fibres of the corresponding Hitchin
fibration in terms of spectral data. Then, we shall define principal
Higgs bundles and look at some examples. Finally, we consider the
particular case of U(p,p) and SU(p,p) Higgs bundles and study the
spectral data. As an application of our results, we shall give a new
geometric description of some of the connected components of the
corresponding moduli space. |