Stable rationality of Brauer-Severi surface bundles

TL;DR

This paper proves that for large enough linear systems on rational surfaces, the general Brauer-Severi surface bundle constructed is not stably rational, highlighting limitations in rationality properties of such bundles.

Contribution

It establishes the non-stable rationality of very general Brauer-Severi surface bundles over rational surfaces for ample linear systems, advancing understanding of rationality obstructions.

Findings

Very general Brauer-Severi surface bundles are not stably rational.

Non-stable rationality holds for sufficiently ample linear systems.

Results contribute to the classification of rationality properties in algebraic geometry.

Abstract

For sufficiently ample linear systems on rational surfaces we show that a very general associated Brauer-Severi surface bundle is not stably rational.