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arXiv · 2602.21861

Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points

Giorgio Navone·Katerina Santicola·Harry C. Shaw·Haowen Zhang
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Abstract

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--Th\'el\`ene, 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.

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Giorgio Navone, Katerina Santicola, Harry C. Shaw, Haowen Zhang. 2026-02-25. Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points. https://arxiv.org/abs/2602.21861

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