Stable rationality and conic bundles (Q303604)

Let \(X\) be a smooth projective variety over an algebraically closed field \(k\), then \(X\) is \textit{stably rational} if \(X\times \mathbb P ^n\) is birational to \(\mathbb P ^{n+\dim X}\) for some \(n\geq 0\). In this paper, the authors prove that certain conic bundles over rational surfaces are not stably rational.