# A remark on algebraic cycles on cubic fourfolds

## TL;DR

This paper explores extending the Clemens-Griffiths criterion, used to prove non-rationality of cubic threefolds, to smooth cubic fourfolds, aiming to deepen understanding of their algebraic cycles.

## Contribution

It proposes a generalization of a classical non-rationality criterion from cubic threefolds to cubic fourfolds, offering new insights into their algebraic cycle structure.

## Key findings

- Proposed a generalized criterion for non-rationality of cubic fourfolds.
- Provided theoretical framework connecting algebraic cycles and rationality.
- Suggested potential applications to classify cubic fourfolds based on rationality.

## Abstract

In this short note we try to generalize the Clemens-Griffiths criterion of non-rationality for smooth cubic threefolds to the case of smooth cubic fourfolds.