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PreprintCC BY 4.0arXiv

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 𝒯 over S is k-rational, provided 𝒯 has k-points. As an application, we obtain examples of stably rational smooth cubic hypersurfaces over β„š in every dimension greater than 2.

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Cite

BibTeXRIS
BibTeX
@misc{tschinkel2026universal,
  title = {{Universal torsors over quartic del Pezzo surfaces and stable rationality}},
  author = {Yuri Tschinkel and Zhijia Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.20029},
  eprint = {2608.20029},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.20029},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Universal torsors over quartic del Pezzo surfaces and stable rationality
AU  - Yuri Tschinkel
AU  - Zhijia Zhang
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.20029
UR  - https://arxiv.org/abs/2608.20029
AB  - Let S be a smooth quartic del Pezzo surface over a field k, of characteristic zero. We prove that a universal torsor 𝒯 over S is k-rational, provided 𝒯 has k-points. As an application, we obtain examples of stably rational smooth cubic hypersurfaces over β„š in every dimension greater than 2.
ER  -