The disk property of coverings of 1-convex surfaces

TL;DR

This paper proves that unbranched coverings of 1-convex surfaces satisfy the discrete disk property if they lack an infinite Nori string of rational curves, contributing to the understanding of complex surface coverings.

Contribution

It establishes a condition under which coverings of 1-convex surfaces satisfy the discrete disk property, specifically excluding infinite Nori strings of rational curves.

Findings

Coverings without infinite Nori strings of rational curves satisfy the discrete disk property.

The result links geometric properties of the covering space to complex analytic properties.

Provides criteria for the discrete disk property in the context of 1-convex surfaces.

Abstract

Let $X$ be an 1-convex surface and $p:\tilde X\to X$ an (unbranched) covering map. We prove that if $\tilde X$ does not contain an infinite Nori string of rational curves then $\tilde X$ satisfies the discrete disk property.