# Closed points on cubic hypersurfaces

## TL;DR

This paper extends previous work on the existence of closed points on cubic hypersurfaces by demonstrating stable birationality of certain symmetric products of these hypersurfaces.

## Contribution

It generalizes Coray's results and establishes stable birationality for symmetric products of cubic hypersurfaces.

## Key findings

- Certain symmetric products of cubic hypersurfaces are stably birational.
- Extension of known results on closed points on cubic hypersurfaces.
- Advances understanding of the birational geometry of cubic hypersurfaces.

## Abstract

We generalize some results of Coray on closed points on cubic hypersurfaces. We show certain symmetric products of cubic hypersurfaces are stably birational.