{"paper":{"title":"On the arithmetic of a family of degree-two K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Christopher Nicholls, Dino Festi, Edgar Costa, Florian Bouyer, Mckenzie West","submitted_at":"2017-03-06T22:01:58Z","abstract_excerpt":"Let $\\mathbb{P}$ denote the weighted projective space with weights $(1,1,1,3)$ over the rationals, with coordinates $x,y,z,$ and $w$; let $\\mathcal{X}$ be the generic element of the family of surfaces in $\\mathbb{P}$ given by \\begin{equation*}\n  X\\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \\end{equation*} The surface $\\mathcal{X}$ is a K3 surface over the function field $\\mathbb{Q}(t)$. In this paper, we explicitly compute the geometric Picard lattice of $\\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\\mathcal{X}$ and other elements of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02127","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}