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Bibliographic Details
Main Author: de Vries, Victor
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.06457
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author de Vries, Victor
author_facet de Vries, Victor
contents 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 Plücker 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 $1$.
format Preprint
id arxiv_https___arxiv_org_abs_2603_06457
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle K3 surfaces over $\mathbb{Q}$ of degree $10$ that have Picard rank $1$
de Vries, Victor
Algebraic Geometry
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 Plücker 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 $1$.
title K3 surfaces over $\mathbb{Q}$ of degree $10$ that have Picard rank $1$
topic Algebraic Geometry
url https://arxiv.org/abs/2603.06457