Split hyperplane sections on smooth polarized K3-surfaces

2025/09/29 by Alex Degtyarev, Degtyarev, Alex
Mathematics · #14J28 (Primary) 14N25 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2509.24349

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We study hyperplane sections of smooth polarized K3-surfaces that split into unions of lines. We describe the dual adjacency graphs of such sections and find sharp upper bounds on their number. In most cases (starting from degree 6), we also compute all configurations of such sections.

Citations

• K3 surfaces of degree six arising from desmic tetrahedra
• Counting Lines with Vinberg's algorithm

Related

• Real split hyperplane sections on smooth polarized K3-surfaces
• Simple isotropic decompositions of the curve sections of the known\n Enriques-Fano threefolds
• On lattice-polarized K3 surfaces
• Note on a Geometric Isogeny of K3 Surfaces
• Stable pair compactification of moduli of K3 surfaces of degree 2