2020/04/23 by David Kohel, Kohel, David, Xavier Roulleau +4
Computer Science · Mathematics · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #math.AG #msc:14J28
paper · pdf · doi:10.48550/arxiv.2004.11421
29 pages; revised version according to the referee's remarks
openalex publication_date 2020/04/23 · arxiv created 2021/05/17 · arxiv updated 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalized Kummer surface X obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a 9A2-configuration of (-2)-curves. Such a configuration plays the role of the 16A1-configurations for usual Kummer surfaces. In this paper we construct 9 other such 9A2-configurations on the generalized Kummer surface associated to the double cover of the plane branched over the sextic dual curve of a cubic curve. The new 9A2-configurations are obtained by taking the pullback of a certain configuration of 12 conics which are in special position with respect to the branch curve, plus some singular quartic curves. We then construct some automorphisms of the K3 surface sending one configuration to another. We also give various models of X and of the generic fiber of its natural elliptic pencil.