Published online by Cambridge University Press: 17 August 2022
In 1977, Gauduchon proved that on every compact hermitian manifold $(X, \omega )$ there exists a conformally equivalent hermitian metric
$\omega _\mathrm {G}$ which satisfies
$\mathrm {dd}^{\mathrm {c}} \omega _\mathrm {G}^{n-1} = 0$. In this note, we extend this result to irreducible compact singular hermitian varieties which admit a smoothing.