2018/04/12 by Marie José Bertin, Bertin, Marie José, Odile Lecacheux +1
Mathematics · #14H52 (Primary) 11G05 (Secondary) #14J27 #14J28 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1804.04394
openalex publication_date 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a generic K3 surface Yk of the Apéry-Fermi pencil, we use the Kneser-Nishiyama technique to determine all its non isomorphic elliptic fibrations. These computations lead to determine those fibrations with 2-torsion sections T. We classify the fibrations such that the translation by T gives a Shioda-Inose structure. The other fibrations correspond to a K3 surface identified by it transcendental lattice. The same problem is solved for a singular member Y2 of the family showing the differences with the generic case. In conclusion we put our results in the context of relations between 2-isogenies and isometries on the singular surfaces of the family.