Tower of coverings of quasi-projective varieties

TL;DR

This paper explores how the geometric properties of a tower of coverings of certain non-compact Kähler manifolds relate to their universal covers, with applications to moduli spaces and symmetric spaces.

Contribution

It establishes a connection between asymptotic geometric properties of covering towers and their universal covers under reasonable assumptions.

Findings

Relates geometric properties of coverings to universal covers.

Applies results to moduli spaces of punctured Riemann surfaces.

Includes Hermitian locally symmetric spaces of finite volume.

Abstract

The main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non-compact K\"ahler manifold of finite volume with reasonable geometric assumptions to its universal covering. Applicable examples include moduli spaces of hyperbolic punctured Riemann surfaces and Hermitian locally symmetric spaces of finite volume.