Non-minimal scalar-flat Kaehler surfaces and parabolic stability
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A 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 Mathematicae
Final version, 30 pages, the appendix has been suppressed and will appear elsewhere, to be published in Inventiones Mathematicae