Order 6 non-symplectic automorphisms of K3 surfaces

2009/12/28 by Jimmy Dillies, Dillies, Jimmy
Mathematics · #14J10 #14J28 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14J10 #msc:14J28 #msc:14J50

paper · pdf · doi:10.48550/arxiv.0912.5228

Rephrased the main theorem to remove a discrepancy with section 9

openalex publication_date 2009/12/28 · arxiv created 2010/08/10 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.

Citations

• K3 surfaces with non-symplectic automorphisms of prime order

Related

• Remarks on K3 surfaces with non-symplectic automorphisms of order 7
• Non-symplectic automorphisms of order multiple of seven on K3 surfaces
• K3 surfaces with non-symplectic automorphisms of prime order
• Symmetries of order four on K3 surfaces
• Non-symplectic automorphisms of order 3 on K3 surfaces