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arXiv · 2603.06457

K3 surfaces over $\mathbb{Q}$ of degree $10$ that have Picard rank $1$

Victor de Vries
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Abstract

We give examples of K3 surfaces over $\mathbb{Q}$ of degree $10$ whose geometric Picard group has rank~$1$. These K3 surfaces are intersections in $\mathbb{P}^9$ of three hyperplanes, one quadric and the image of the Pl\"ucker embedding of the Grasmannian $\mathrm{Gr}(2,5)$. We also give an example of a K3 surface of degree $6$ over~$\mathbb{Q}$ whose Picard rank is $1$.

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Victor de Vries. 2026-03-06. K3 surfaces over $\mathbb{Q}$ of degree $10$ that have Picard rank $1$. https://arxiv.org/abs/2603.06457

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