Hilbert property for low-genus families and degree-one del Pezzo surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909965909753856 |
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| author | Demeio, Julian Streeter, Sam Winter, Rosa |
| author_facet | Demeio, Julian Streeter, Sam Winter, Rosa |
| contents | We prove that the Hilbert property is satisfied by certain del Pezzo surfaces of degree one and Picard rank 1 over fields finitely generated over $\mathbb{Q}$. We generalize results of the first author on elliptic surfaces and employ constructions used by Desjardins and the third author to prove density of rational points. Our results are the first on the Hilbert property for minimal del Pezzo surfaces of degree one without a conic fibration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert property for low-genus families and degree-one del Pezzo surfaces Demeio, Julian Streeter, Sam Winter, Rosa Algebraic Geometry Number Theory 14G05, 14J20 (primary), 14G25, 14G27, 11G35 (secondary) We prove that the Hilbert property is satisfied by certain del Pezzo surfaces of degree one and Picard rank 1 over fields finitely generated over $\mathbb{Q}$. We generalize results of the first author on elliptic surfaces and employ constructions used by Desjardins and the third author to prove density of rational points. Our results are the first on the Hilbert property for minimal del Pezzo surfaces of degree one without a conic fibration. |
| title | Hilbert property for low-genus families and degree-one del Pezzo surfaces |
| topic | Algebraic Geometry Number Theory 14G05, 14J20 (primary), 14G25, 14G27, 11G35 (secondary) |
| url | https://arxiv.org/abs/2510.13967 |