Singular Gauduchon metrics and Hermite-Einstein problem on non-Kähler varieties

Abstract: 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 the study of the existence of Hermite-Einstein metrics and the classification of non-Kähler surfaces. In this talk, I will first introduce the 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.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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