arXiv subjects

Giorgio Navone

Publications and source records attributed to Giorgio Navone.

2 recordsLinked to original sources

arXiv2026

Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points

We construct an infinite family of quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ with no quadratic points, for all primes $p\neq 2$. This answers a question of Colliot--Th\'el\`ene, Creutz and Viray in the negative, which asks whether every quartic del Pezzo surface has quadratic points over $C_2$ fields. We exhibit a Brauer--Manin obstruction on the variety parametrising lines associated to the quartic del Pezzo surface.

math.NT↗

arXiv2025

Transcendental Brauer groups of cubic generalised Kummer surfaces

Given a cubic curve $C$ over a number field, we consider the K3 surface $Y_C$ constructed as the minimal desingularisation of the quotient of $C \times C$ by an automorphism of order 3. We relate the transcendental Brauer groups of $Y_C$ and $C \times C$, allowing us to explicitly compute the former group in the case of a diagonal cubic curve defined over $\mathbb{Q}$. We obtain conjectural insight on the existence of Galois cubic points over $\mathbb{Q}$ for everywhere locally soluble diagonal cubic curves.

math.NT↗