Free dihedral actions on Abelian varieties

TL;DR

This paper presents a straightforward method to construct hyperelliptic varieties as quotients of complex tori by dihedral group actions that have no fixed points or translations, extending previous work for specific cases.

Contribution

It generalizes earlier constructions of hyperelliptic varieties by providing a simple approach for dihedral groups of arbitrary dimension.

Findings

Constructed hyperelliptic varieties as quotients of complex tori by dihedral groups.

Extended previous specific case constructions to more general dihedral groups.

Provided a new framework for understanding symmetries in complex tori and hyperelliptic varieties.

Abstract

We give a simple construction for hyperelliptic varieties defined as the quotient of a complex torus by the action of a dihedral group that contains no translations and fixes no points. This generalizes a construction given by Catanese and Demleitner for $D_4$ in dimension three.