Elliptic fibrations and symplectic automorphisms on K3 surfaces

2008/01/25 by Alice Garbagnati, A. Sarti, Garbagnati, Alice +1
Mathematics · #14J10 #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.0801.3992

openalex publication_date 2008/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U³⊕ E₈(-1)² depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces.

Citations

• Symplectic Automorphisms on Kummer Surfaces

Related

• Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms
• Symplectic automorphisms and the Picard group of a K3 surface
• K3 surfaces with a symplectic automorphism of order 11
• On some K3 surfaces with order sixteen automorphism
• K3-surfaces with special symmetry