  The twice-dimensionally reduced Seiberg-Witten monopole equations admit
solutions depending on two real parameters (b,c) and an arbitrary analytic
function f(z) determining a solution of Liouville's equation. The U(1) and
manifold curvature 2-forms F and R^1_2 are invariant under fractional SL(2,R)
transformations of f(z). When b=1/2 and c=0 and f(z) is the Fuchsian function
uniformizing an algebraic function whose Riemann surface has genus p \geq 2 ,
the solutions, now SL(2,R) invariant, are the same surfaces accompanied by a
U(1) bundle of c_1=\pm (p-1) and a 1-component constant spinor.
