2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126784We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates this conjecture, and an example computation that supports it.13 pages, v3: fixed typosAlgebraic GeometryDifferential Geometry53C55; 53C25text