Beyond the square-root barrier: cubic forms of Perazzo type

TL;DR

This paper demonstrates the application of the circle method to analyze rational points on a specific cubic fourfold, surpassing traditional limitations known as the square-root barrier.

Contribution

It introduces a novel approach using the circle method to study rational points on cubic fourfolds beyond the square-root barrier.

Findings

Successfully applied the circle method to a cubic fourfold.

Achieved results that go beyond the traditional square-root barrier.

Provides new insights into rational points on cubic fourfolds.

Abstract

We show how the circle method can be used to study rational points on a certain cubic fourfold, going beyond the square-root barrier.