2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98126A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that CP^2 blown up at 10 suitably chosen points, admits a scalar-flat Kaehler metric; this answers a question raised by Claude LeBrun in 1986 in connection with the classification of compact self-dual 4-manifolds.Final version, 30 pages, the appendix has been suppressed and will appear elsewhere, to be published in Inventiones MathematicaeDifferential GeometryAlgebraic Geometry53C55; 53C25; 53C20; 53C21; 14E15text