Singular Gauduchon metrics

In 1977, Gauduchon proved that on every compact hermitian manifold $(X, \omega )$ there exists a conformally equivalent metric $\omega _\mathrm {G}$ which satisfies $\mathrm {dd}^{\mathrm {c}} {G}^{n-1} = 0$ . this note, we extend result to irreducible singular varieties admit smoothing.