Bergman Type Metrics in Tower of Coverings

TL;DR

This paper proves a new version of a classical statement related to Bergman type metrics in tower coverings, leading to a clearer uniformization theorem in complex algebraic geometry.

Contribution

It introduces a novel formulation of Kazhdan's statement and simplifies the uniformization theorem in the context of complex algebraic geometry.

Findings

New version of Kazhdan's statement established

Simplified form of the uniformization theorem obtained

Enhanced understanding of Bergman metrics in tower coverings

Abstract

We establish a version of a statement attributed to Kazhdan by Yau. As a corollary, we obtain a more transparent form of our uniformization theorem in complex algebraic geometry.