2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141912We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum of five reverse-oriented complex projective planes admits such metrics.37 pages, 5 figuresDifferential GeometryComplex Variables53C25; 30F40text