Singular Gauduchon metrics

TL;DR

This paper extends Gauduchon's classical result on the existence of special hermitian metrics to singular hermitian varieties that can be smoothed, broadening the scope of geometric analysis on complex varieties.

Contribution

It generalizes the existence of Gauduchon metrics from smooth to certain singular hermitian varieties with smoothing properties.

Findings

Existence of Gauduchon metrics on singular varieties with smoothing

Extension of classical results to singular complex geometry

Broader applicability of hermitian metric theory

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.