Generalized Shioda-Inose Structures on K3 Surfaces

1998/09/16 by Hurşit Önsiper, H. Onsiper, Onsiper, H. +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AG

paper · pdf · doi:10.48550/arxiv.math/9809083

LaTeX 2.09, 5 pages, To appear in Manuscripta Math

arxiv created 1998/09/16 · openalex publication_date 1998/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the finite group actions on K3 and Abelian surfaces giving the same orbit space after desingularization. We show that when the group is not Z₂, then the Picard number of the K3 surface must be 19 or 20, and that in the latter case the Abelian surface is uniquely determined by the K3 surface.

Related

• Generalized Shioda--Inose structures of order 3
• Group Actions, Cyclic Coverings and Families of K3-Surfaces
• K3 surfaces with action of the group M₂₀
• Elliptic fibrations and symplectic automorphisms on K3 surfaces
• Elliptic K3 surfaces admitting a Shioda-Inose structure