Strongly Cyclic Coverings of Cyclic Curves

TL;DR

This paper introduces unramified strongly cyclic coverings of cyclic curves, extending existing theorems, and provides explicit equations, isomorphism criteria, and ramification analysis for these coverings.

Contribution

It defines unramified strongly cyclic coverings, extends prior theorems to this broader class, and offers explicit models and classification criteria.

Findings

Defined unramified strongly cyclic coverings.

Extended theorems to this new class.

Provided explicit equations and isomorphism conditions.

Abstract

In this note, we introduce the notion of an unramified strongly cyclic covering for a cyclic curve, a class that has similar properties to, and contains, unramified double covers of hyperelliptic curves. We determine several of their basic properties, extending the theorems in \cite{MR2217998} to this larger class. In particular, we will write down equations for smooth affine models, determine when they are isomorphic, and discuss the curves that they are ramified cyclic covers of.