Mordell-Weil groups and automorphism groups of elliptic K3 surfaces

2022/10/04 by Ichiro Shimada, Shimada, Ichiro · 1 citation
Mathematics · #14J28 #14Q10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2210.01328

openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a method to calculate the action of the Mordell-Weil group of an elliptic K3 surface on the numerical Néron-Severi lattice of the K3 surface. As an application, we compute a finite generating set of the automorphism group of a K3 surface birational to the double plane branched along a 6-cuspidal sextic curve of torus type.

Cited by

• Enriques surfaces with non-generic non-degeneracy

Related

• On the geometry of K3 surfaces with finite automorphism group and no elliptic fibrations
• On elliptic K3 surfaces
• An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces
• Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms
• The automorphism groups of certain singular K3 surfaces and an Enriques surface