2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147609It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.9 pages, latex, with \Bbb font redefined for WWW useDifferential GeometryAlgebraic Geometrytext