Kummer covers and braid monodromy

TL;DR

This paper presents a method to reconstruct braid monodromy of curves under Kummer covers, combining techniques for non-generic to generic monodromy conversion, applicable beyond Kummer covers with explicit examples.

Contribution

It introduces a novel approach to reconstruct braid monodromy for Kummer covers and a general 'generification' method for non-generic to generic monodromy conversion.

Findings

Successfully reconstructs braid monodromy for specific curves

Develops a systematic method for generification of braid monodromy

Provides explicit examples demonstrating the techniques

Abstract

In this work we describe a method to reconstruct the braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting, since it combines two techniques, namely, the reconstruction of a highly non-generic braid monodromy with a systematic method to go from a non-generic to a generic braid monodromy. This "generification" method is independent from Kummer covers and can be applied in more general circumstances since non generic braid monodromies appear more naturally and are oftentimes much easier to compute. Explicit examples are computed using these techniques.