  We extend the previous treatment of Liouville theory on the torus, to the
general case in which the distribution of charges is not necessarily symmetric.
This requires the concept of Fuchsian differential equation on Riemann
surfaces. We show through a group theoretic argument that the Heun parameter
and a weight constant are sufficient to satisfy all monodromy conditions. We
then apply the technique of differential equation on a Riemann surface to the
two point function on the torus in which one source is arbitrary and the other
small. As a byproduct we give in terms of quadratures the exact Green function
on the square and on the rhombus with opening angle 2 pi/6 in the background of
the field generated by an arbitrary charge.
