Séminaire de Géométrie Complexe

Singular Gauduchon metrics

by Chung-Ming Pan

Pellos (IMT)



Gauduchon metrics are useful generalizations of Kähler metrics in non-Kähler geometry. In this talk, we will present the work in which we obtain the existence of Gauduchon metrics on compact hermitian varieties admitting a smoothing. This result generalizes Gauduchon’s theorem which says that on a compact complex manifold, one can find a Gauduchon metric in every conformal class of hermitian metrics. If time permits, we will explain an application that gives a partial solution to a conjecture proposed by Di Nezza-Guedj-Guenancia.