Let X be a Riemann surface of genus g greater or equal than 2.
A twisted U(p,q)-Higgs bundle consists of a pair of holomorphic vector
bundles on a Riemann surface, together with a pair of twisted maps
between them. Here we study the variation with the parameter of the
moduli space of twisted U(p,q)-Higgs bundles with a view to obtaining
birationality results.