Rationalit\'e d'un fibr\'e en coniques

TL;DR

This paper proves the rationality of a specific conic bundle associated with a threefold, resolving a question about its rationality status that was previously unknown.

Contribution

The paper demonstrates the rationality of a particular conic bundle linked to a threefold, advancing understanding of its birational properties.

Findings

The conic bundle is rational.

The threefold is birational to a rational conic bundle.

The rationality question posed by F. Campana is answered affirmatively.

Abstract

F. Campana had asked whether a certain threefold is rational. In arXiv:1310.3569v1 [mathAG], this variety was shown to be birational to a specific conic bundle and then to be unirational. We prove that this conic bundle is rational.