The Classification of Rigid Hyperelliptic Fourfolds

TL;DR

This paper classifies rigid hyperelliptic fourfolds, describing them explicitly as quotients of Fermat elliptic curves, and distinguishes them up to biholomorphism and diffeomorphism.

Contribution

It provides a detailed classification of rigid hyperelliptic fourfolds, explicitly describing their structure as finite étale quotients of Fermat elliptic curves.

Findings

Classification of rigid hyperelliptic fourfolds up to biholomorphism and diffeomorphism

Explicit description as finite étale quotients of Fermat elliptic curves

Identification of their geometric and topological properties

Abstract

We provide a fine classification of rigid hyperelliptic manifolds in dimension four up to biholomorphism and diffeomorphism. These manifolds are explicitly described as finite \'etale quotients of a product of four Fermat elliptic curves.