Stable rationality of higher dimensional conic bundles

TL;DR

This paper proves that most high-dimensional conic bundles over projective space are not stably rational when their anti-canonical divisor isn't ample, expanding understanding of rationality in algebraic geometry.

Contribution

It establishes non-stable rationality for very general nonsingular conic bundles in higher dimensions under specific anti-canonical conditions.

Findings

Very general conic bundles are not stably rational when anti-canonical divisor is not ample.

Results apply for dimensions n ≥ 3.

Advances the classification of rationality properties in algebraic geometry.

Abstract

We prove that a very general nonsingular conic bundle $X\rightarrow\mathbb{P}^{n-1}$ embedded in a projective vector bundle of rank $3$ over $\mathbb{P}^{n-1}$ is not stably rational if the anti-canonical divisor of $X$ is not ample and $n\geq 3$.