Non-thin rational points for elliptic K3 surfaces

2024/04/10 by Damián Gvirtz, Gvirtz-Chen, Damián, Giacomo Mezzedimi +1 · 3 citations
Arts and Humanities · Mathematics · #06B05 (Secondary) #11R45 #14G05 (Primary) 14J27 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.06844

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that elliptic K3 surfaces over a number field which admit a second elliptic fibration satisfy the potential Hilbert property. Equivalently, the set of their rational points is not thin after a finite extension of the base field. Furthermore, we classify those families of elliptic K3 surfaces over an algebraically closed field which do not admit a second elliptic fibration.

Cited by

• Hilbert properties of varieties
• Hilbert property for low-genus families and degree-one del Pezzo surfaces
• Rank jumps and Multisections of elliptic fibrations on K3 surfaces

Related

• Elliptic Fibrations and Hilbert Property
• K3 surfaces, rational curves, and rational points
• Non-rational varieties with the Hilbert Property
• Density of rational points on elliptic K3 surfaces
• Elliptic fibrations of some extremal K3 surfaces