The author defines the critical metrics relative to the algebraic torus \(T\) and the stable subvariety \(M_n\) relative to \(T\) of the set \(P^\ast(V_m)\) of all hyperplanes through the origin in \(V_m\). The main theorem of this paper asserts that a subvariety \(M_n\) of \(P(V_m)\) is stable relative to \(T\) if and only if there exists a critical metric \(\omega\in S\) relative to \(T\).