The $L$-function of the surface parametrizing cuboids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910066987237376 |
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| author | Horie, Madoka Yamauchi, Takuya |
| author_facet | Horie, Madoka Yamauchi, Takuya |
| contents | In this note, we compute the $L$-function of the projective smooth surface $S$ over $\mathbb{Q}$ that parametrizes cuboids whose geometric properties are studied in detail by Stoll and Testa. As a byproduct, we completely determine the structure of ${\rm Pic}(S_{\overline{\mathbb{Q}}})$ as a ${\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$-module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L$-function of the surface parametrizing cuboids Horie, Madoka Yamauchi, Takuya Number Theory Algebraic Geometry In this note, we compute the $L$-function of the projective smooth surface $S$ over $\mathbb{Q}$ that parametrizes cuboids whose geometric properties are studied in detail by Stoll and Testa. As a byproduct, we completely determine the structure of ${\rm Pic}(S_{\overline{\mathbb{Q}}})$ as a ${\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$-module. |
| title | The $L$-function of the surface parametrizing cuboids |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2512.22520 |