On the arithmetic of a family of degree-two K3 surfaces

2017/03/06 by Florian Bouyer, Edgar Costa, Bouyer, Florian +7
Arts and Humanities · Mathematics · Social Sciences · #11G35 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · doi:10.48550/arxiv.1703.02127

openalex publication_date 2017/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ℙ denote the weighted projective space with weights (1,1,1,3) over the rationals, with coordinates x,y,z, and w; let X be the generic element of the family of surfaces in ℙ given by X\colon w²=x⁶+y⁶+z⁶+tx²y²z². The surface X is a K3 surface over the function field ℚ(t). In this paper, we explicitly compute the geometric Picard lattice of X, together with its Galois module structure, as well as derive more results on the arithmetic of X and other elements of the family X.

Citations

• The surface parametrizing cuboids

Related

• A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree 2
• Picard lattices of families of K3 surfaces
• Study on the family of K3 surfaces induced from the lattice (D₄)³ ⊕ < -2 > ⊕ < 2 >
• K3 surfaces with Picard number one and infinitely many rational points
• K3 surfaces with two involutions and low Picard number