Universal torsors over quartic del Pezzo surfaces and stable rationality

Yuri Tschinkel; Zhijia Zhang

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arXiv · 2608.20029

Universal torsors over quartic del Pezzo surfaces and stable rationality

Yuri Tschinkel·Zhijia Zhang

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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.

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BibTeX RIS

Yuri Tschinkel, Zhijia Zhang. 2026-08-20. Universal torsors over quartic del Pezzo surfaces and stable rationality. https://arxiv.org/abs/2608.20029

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