Singular Gauduchon metrics

Abstract

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

16 pages; v2: added an example in section 1, corrected a few typos

Cited by in corpus (1)

• Families of singular Chern-Ricci flat metrics