Hilbert property for low-genus families and degree-one del Pezzo surfaces

Julian Demeio; Sam Streeter; Rosa Winter

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arXiv · 2510.13967

Hilbert property for low-genus families and degree-one del Pezzo surfaces

Julian Demeio·Sam Streeter·Rosa Winter

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Abstract

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.

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Julian Demeio, Sam Streeter, Rosa Winter. 2025-10-15. Hilbert property for low-genus families and degree-one del Pezzo surfaces. https://arxiv.org/abs/2510.13967

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