We discuss geometrical aspects of Higgs systems and Toda field theory
in the framework of the theory of vector bundles on Riemann surfaces o
f genus greater than one. We point out how Toda fields can be consider
ed as equivalent to Higgs systems - a connection on a vector bundle E
together with an End(E)-valued one form both in the standard and in th
e Conformal Affine case. We discuss how variations of Hedge structures
can arise in such a framework and determine holomorphic embeddings of
Riemann surfaces into locally homogeneous spaces, thus giving hints t
o possible realizations of W-n-geometries.