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arXiv · 2408.08436

Quartic del Pezzo surfaces without quadratic points

Brendan Creutz·Bianca Viray
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Abstract

Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$ (i.e., has a closed point of degree $2$ modulo $4$),, and asked whether such surfaces always have a closed point of degree $2$. We resolve this by constructing infinitely many quartic del Pezzo surfaces over $\mathbb{Q}$ without degree $2$ points. These are the first examples of smooth intersections of two quadrics with index strictly less than the minimal degree of a closed point.

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Brendan Creutz, Bianca Viray. 2024-08-15. Quartic del Pezzo surfaces without quadratic points. https://doi.org/10.2140/pjm.2025.337.215

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