# On forms of the Segre cubic

## TL;DR

This paper investigates the forms of the Segre cubic over non-algebraically closed fields, focusing on their automorphism groups and birational properties, revealing that all forms are cubic hypersurfaces with points.

## Contribution

It proves that all forms of the Segre cubic are cubic hypersurfaces and possess points, advancing understanding of their structure over various fields.

## Key findings

- All forms are cubic hypersurfaces.
- Every form has at least one rational point.
- Automorphism groups are characterized for these forms.

## Abstract

In this article we study forms of the Segre cubic over non-algebraically closed fields, their automorphism groups and equivariant birational rigidity. In particular, we show that all forms of the Segre cubic are cubic hypersurfaces and all of them have a point.