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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.06457 |
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| _version_ | 1866914375668858880 |
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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 |