Abstract

In this talk, I will begin by reviewing the definition of Gauduchon metrics and some progress on the correspondence between the existence of Hermite-Einstein metrics and the stability notion over singular bundles/spaces. I will then introduce a singular version of Gauduchon's theorem and discuss its application to the Hermite-Einstein problem for reflexive sheaves (which can be recognized as a singular holomorphic vector bundle) satisfying the slope-stability condition on non-Kähler normal varieties. Finally, 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.

 

Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo  (NTU), Chung-Jun Tsai (NTU)