Branching Data for Algebraic Functions and Representability by Radicals

TL;DR

This paper reviews recent and classical work on how the branching data of algebraic functions determines their expressibility by radicals, providing criteria for such representability.

Contribution

It introduces specific branching data conditions that guarantee algebraic functions are representable by radicals, building on recent and classical results.

Findings

Identifies branching data ensuring radical representability.

Connects branching data with classical Ritt's work.

Provides criteria for algebraic functions to be expressible by radicals.

Abstract

The branching data of an algebraic function is a list of orders of local monodromies around branching points. We present branching data that ensure that the algebraic functions having them are representable by radicals. This paper is a review of recent work by the authors and of closely related classical work by Ritt.