K3 surfaces with a symplectic automorphism of order 11

2006/02/23 by Igor Dolgachev, Dolgachev, Igor, JongHae Keum +1
Mathematics · #14J28 #20B25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.math/0602518

openalex publication_date 2006/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify possible finite groups of symplectic automorphisms of K3 surfaces of order divisible by 11. The characteristic of the ground field must be equal to 11. The complete list of such groups consists of five groups: the cyclic group of order 11, 11\rtimes 5, L₂(11) and the Mathieu groups M₁₁, M₂₂. We also show that a surface X admitting an automorphism g of order 11 admits a g-invariant elliptic fibration with the Jacobian fibration isomorphic to one of explicitly given elliptic K3 surfaces.

Related

• Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms
• The automorphism groups of certain singular K3 surfaces and an Enriques surface
• Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic
• K3 surfaces with an automorphism of order 11
• Elliptic fibrations and symplectic automorphisms on K3 surfaces