Extension of analytic covers by extension of their ramification divisor

TL;DR

This paper establishes new theorems for extending analytic covers by focusing on the extension of their ramification divisors, including Thullen-type and Hartogs-type extension results.

Contribution

It introduces a novel extension theorem for analytic covers that relies solely on extending the ramification divisor, advancing the theory of cover extensions.

Findings

Topological extension theorems for analytic covers

Extension of ramification divisors suffices for cover extension

Thullen-type and Hartogs-type extension theorems proved

Abstract

This paper deals with extension of analytic covers. We prove topological extension theorems for analytic covers. The main result is an extension theorem which only uses the extension of the ramification divisor. We give also a Thullen-type and a Hartogs-type extensions theorems.