  To each connected component in the space of semisimple representations from
the orbifold fundamental group of the base orbifold of a Seifert fibered
homology 3-sphere into the Lie group U(2,1), we associate a real number called
the "orbifold Toledo invariant." For each such orbifold, there exists an
elliptic surface over it, called a Dolgachev surface. Using the theory of Higgs
bundles on these Dolgachev surfaces, we explicitly compute all values taken on
by the orbifold Toledo invariant.
