# The classification of Hyperelliptic threefolds

## TL;DR

This paper completes the classification of hyperelliptic threefolds, specifically describing those with group D_4, highlighting their algebraic nature and their place within a 2-dimensional family.

## Contribution

It provides a complete and elementary classification of hyperelliptic threefolds with group D_4, including their algebraic properties and family structure.

## Key findings

- Hyperelliptic threefolds with group D_4 form an irreducible 2-dimensional family.
- The classification is elementary and self-contained.
- These threefolds are algebraic.

## Abstract

We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group $D_4$. These are algebraic and form an irreducible 2-dimensional family. Our paper is fully self-contained.