Rationality of Brauer-Severi surface bundles over rational 3-folds

TL;DR

This paper establishes conditions under which certain algebraic surface bundles over rational three-dimensional varieties are not stably rational, providing explicit examples and demonstrating the existence of non-stably rational families.

Contribution

It offers a new sufficient condition for non-stable rationality of Brauer-Severi surface bundles over rational 3-folds and constructs explicit examples illustrating this.

Findings

Identified a sufficient condition for non-stable rationality.

Constructed explicit examples satisfying this condition.

Proved the existence of families with non-stably rational general members.

Abstract

We give a sufficient condition for a Brauer-Severi surface bundle over a rational 3-fold to not be stably rational. Additionally, we present an example that satisfies this condition and demonstrate the existence of families of Brauer-Severi surface bundles whose general members are smooth and not stably rational.