Universal torsors over quartic del Pezzo surfaces and stable rationality

Abstract

Let $S$ be a smooth quartic del Pezzo surface over a field $k$, of characteristic zero. We prove that a universal torsor $\mathcal{T}$ over $S$ is $k$-rational, provided $\mathcal{T}$ has $k$-points. As an application, we obtain examples of stably rational smooth cubic hypersurfaces over $\mathbb{Q}$ in every dimension greater than 2.

25 pages