Lines on K3-sextics with simple singularities

2025/12/08 by Degtyarev, Alex, Rams, Sławomir
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary: 14J28 #Secondary: 14N25

paper · doi:10.48550/arxiv.2512.08018

openalex publication_date 2025/12/08 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

We advance our understanding of the configurations of low degree smooth rational curves on (quasi-)polarized complex K3-surfaces. We apply our efficient approach to classify the configurations of at least 36 lines on K3-sextics with at worst A-D-E singularities. Besides, we characterize a certain class of infinite dihedral groups of birational automorphisms of K3-sextics, we show that no K3-sextic can contain a Kummer configuration of lines, and we give a complete account of the line configurations on closest analogue of Kummer K3-octics or quartics, viz. the so-called Humbert K3-sextics.

Citations

• K3 surfaces of degree six arising from desmic tetrahedra
• Counting Lines with Vinberg's algorithm
• On the Classification of K3-Surfaces with Nine Cusps
• Mirror symmetry for lattice polarized K3 surfaces

Related

• Low degree rational curves on quasi-polarized K3 surfaces
• K3 surfaces of degree six arising from desmic tetrahedra
• K3 surfaces of Kummer type in characteristic two
• Curves with low Harbourne constants on Kummer and Abelian surfaces
• A Sextic with 35 Cusps