Uniformization of klt pairs by bounded symmetric domains

TL;DR

This paper characterizes when certain complex algebraic pairs are uniformized by bounded symmetric domains, providing criteria and applications to orbifold quotients and classical domains using Chern class equalities.

Contribution

It establishes necessary and sufficient conditions for klt pairs with ample canonical bundle to be uniformized by bounded symmetric domains, advancing the understanding of their geometric structure.

Findings

Characterization of klt pairs uniformized by bounded symmetric domains

Criteria for orbifold quotients of polydisc and classical domains

Use of Miyaoka-Yau-type Chern equalities for classification

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.