Free dihedral actions on abelian varieties

Abstract

We give a simple construction for hyperelliptic varieties, defined as the quotient of a complex torus by the action of a finite group $G$ that contains no translations and acts freely, with $G$ any dihedral group. This generalizes a construction given by Catanese and Demleitner for $D_4$ in dimension three.

Keywords

• abelian varieties
• dihedral group
• free action