Uniform rationality of products with the plane

TL;DR

This paper proves that the product of a nonsingular rational variety with the plane is uniformly rational, implying that stably rational varieties are also stably uniformly rational.

Contribution

It establishes the uniform rationality of products of nonsingular rational varieties with the plane, advancing understanding of rationality properties.

Findings

$X \times \mathbb{C}^2$ is uniformly rational for nonsingular rational $X$

Nonsingular stably rational varieties are stably uniformly rational

Provides new insights into the structure of rational varieties

Abstract

Let $X$ be a nonsingular rational variety. We prove that $X\times \mathbb{C}^2$ is uniformly rational. It follows that nonsingular stably rational varieties are stably uniformly rational.