# Chirality of Real Non-singular Cubic Fourfolds and Their Pure Deformation Classification

## TL;DR

This paper provides a detailed classification of real non-singular cubic fourfolds, focusing on their chirality properties and identifying which cannot be deformed into their mirror images.

## Contribution

It offers a complete deformation classification of these hypersurfaces, specifically addressing the chirality problem for the first time.

## Key findings

- Identified which real cubic fourfolds are chiral or achiral.
- Developed a refined classification scheme for these hypersurfaces.
- Provided criteria for non-deformability to mirror images.

## Abstract

In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.