Coverings over Tori and Topological Approach to Klein's Resolvent Problem

TL;DR

This paper investigates how coverings over a topological torus relate to those over lower-dimensional spaces and applies these insights to identify obstructions in simplifying algebraic equations via rational transformations.

Contribution

It provides a topological characterization of coverings over tori and applies this to algebraic geometry to find obstructions to parameter reduction in equations.

Findings

Characterization of coverings over tori induced from lower-dimensional spaces

Identification of obstructions in transforming algebraic equations with parameters

Application of topological methods to algebraic geometric problems

Abstract

This work answers the question what coverings over a topological torus can be induced from a covering over a space of dimension $k$. The answer to this question is then applied in algebro-geometric context to present obstructions to transforming an algebraic equation depending on several parameters to an equation depending on less parameters by means of a rational transformation.