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Singular Gauduchon metrics
- Part of
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- Journal:
- Compositio Mathematica / Volume 158 / Issue 6 / June 2022
- Published online by Cambridge University Press:
- 17 August 2022, pp. 1314-1328
- Print publication:
- June 2022
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- Article
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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.
