# Teichm\"uller spaces of Generalized Hyperelliptic Manifolds

## TL;DR

This paper characterizes the connected components of Teichmüller space for generalized hyperelliptic manifolds, which are quotients of complex tori by finite group actions, linking them to specific Euclidean crystallographic groups.

## Contribution

It provides a detailed description of the connected components of Teichmüller space for these manifolds, connecting geometric structures with group actions and crystallographic groups.

## Key findings

- Connected components of Teichmüller space are characterized.
- Generalized hyperelliptic manifolds are quotients of complex tori by finite groups.
- The classification relates to torsion-free, even Euclidean crystallographic groups.

## Abstract

In this paper we achieve a description of the connected components of Teichm\"uller space corresponding to Generalized Hyperelliptic Manifolds $X$. These are the quotients $ X = T/G$ of a complex torus $T$ by the free action of a finite group $G$, and they are also the K\"ahler classifying spaces for a certain class of Euclidean cristallographic groups $\Gamma$, the ones which are torsion free and even.