Extremal metrics and K-stability

We propose an algebraic geometric stability criterion for apolarised variety to admit an extremal Kähler metric. Thisgeneralises conjectures by Yau, Tian and Donaldson, which relateto the case of Kähler–Einstein and constant scalarcurvature metrics. We give a result in geometric invariant theorythat motivates this conjecture, and an example computation thatsupports it.