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.
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