Abelian automorphism groups of cubic fourfolds

TL;DR

This paper classifies all finite abelian groups that can act effectively on smooth cubic fourfolds, providing a comprehensive list of such symmetry groups.

Contribution

It provides the first complete classification of abelian automorphism groups of smooth cubic fourfolds, filling a gap in the understanding of their symmetries.

Findings

Complete list of finite abelian groups acting on smooth cubic fourfolds

Identification of effective automorphism groups for these fourfolds

Foundation for further symmetry and moduli space studies

Abstract

We list all finite abelian groups which act effectively on smooth cubic fourfolds.