Uniformization of projective klt varieties by bounded symmetric domains

Abstract

Using results from non-abelian Hodge theory for klt spaces developed by Greb, Kebekus, Peternell and Taji, we deduce necessary and sufficient conditions for projec tive varieties with klt singularities to be uniformized by bounded symmetric domains. This generalizes a well known result of Simpson to the singular setting. We apply this to obtain explicit Miyaoka-Yau-type equalities to characterize singular quotients of the four classical irreducible bounded symmetric domains, and the polydisk.