Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866912926625955840 |
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| author | Navone, Giorgio Santicola, Katerina Shaw, Harry C. Zhang, Haowen |
| author_facet | Navone, Giorgio Santicola, Katerina Shaw, Harry C. Zhang, Haowen |
| contents | We construct an infinite family of quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ with no quadratic points, for all primes $p\neq 2$. This answers a question of Colliot--Thélène, Creutz and Viray in the negative, which asks whether every quartic del Pezzo surface has quadratic points over $C_2$ fields. We exhibit a Brauer--Manin obstruction on the variety parametrising lines associated to the quartic del Pezzo surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21861 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points Navone, Giorgio Santicola, Katerina Shaw, Harry C. Zhang, Haowen Number Theory Algebraic Geometry 14G05, 14G12, 14G17 We construct an infinite family of quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ with no quadratic points, for all primes $p\neq 2$. This answers a question of Colliot--Thélène, Creutz and Viray in the negative, which asks whether every quartic del Pezzo surface has quadratic points over $C_2$ fields. We exhibit a Brauer--Manin obstruction on the variety parametrising lines associated to the quartic del Pezzo surface. |
| title | Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points |
| topic | Number Theory Algebraic Geometry 14G05, 14G12, 14G17 |
| url | https://arxiv.org/abs/2602.21861 |