Uniformization of klt pairs by bounded symmetric domains

Abstract

Given a complex-projective klt pair $(X,\Delta )$ with standard coefficients and such that $K_X+\Delta$ is ample, we determine necessary and sufficient conditions for the pair $(X,\Delta )$ to be uniformized by a bounded symmetric domain. As an application, we obtain characterizations of orbifold quotients of the polydisc and of the four classical irreducible bounded symmetric domains in terms of Miyaoka-Yau-type Chern equalities.