  Let M=P(E) be a ruled surface. We introduce metrics of finite volume on M
whose singularities are parametrized by a parabolic structure over E. Then, we
generalise results of Burns--de Bartolomeis and LeBrun, by showing that the
existence of a singular Kahler metric of finite volume and constant non
positive scalar curvature on M is equivalent to the parabolic polystability of
E; moreover these metrics all come from finite volume quotients of $H^2 \times
CP^1$. In order to prove the theorem, we must produce a solution of
Seiberg-Witten equations for a singular metric g. We use orbifold
compactifications $\overline M$ on which we approximate g by a sequence of
smooth metrics; the desired solution for g is obtained as the limit of a
sequence of Seiberg-Witten solutions for these smooth metrics.
