KASS seminar

Abstrakt: Gauduchon metrics are very useful generalizations of Kähler metrics in non-Kähler geometry, as Gauduchon proved that these special metrics always exist on compact complex manifolds. One of their important applications is defining the notion of stability for vector bundles/ sheaves on non-Kähler manifolds. It also leads to the study of the existence of Hermite-Einstein metrics and the classification of non-Kähler surfaces. In this talk, I will first introduce a singular version of Gauduchon's theorem and its application to the Hermite-Einstein problem for stable reflexive sheaves on non-Kähler normal varieties. Then, I will explain one of the main technical points that lies in obtaining uniform Sobolev inequalities for perturbed hermitian metrics on a resolution of singularities.