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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Commutative Algebra and Its Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 20 August 2026
- Document type
- Preprint