Line configurations and K3 surfaces

2023/09/27 by Elias Sink, Sink, Elias · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2312.07542

openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the realization spaces of 10₃ line configurations. Answering a question posed by Sturmfels in 1991, we use elliptic surface techniques to show that realizations over ℚ are dense in those over ℝ for all 10₃ configurations. We find that for exactly four of the ten configurations, the realization space admits a compactification by a K3 surface. We show that these have Picard number 20 and compute their discriminants. Finally, we use geometric invariant theory to give an elegant interpretation of these K3 surfaces as moduli spaces.

Cited by

• Configurations of 10 points and their incidence varieties

Related

• Topology of Real Schlafli Six-Line Configurations on Cubic Surfaces and\n in mathbbRP³
• Picard lattices of families of K3 surfaces
• K3 surfaces over small number fields and Kummer constructions in families
• Compact moduli of elliptic K3 surfaces
• Note on a Geometric Isogeny of K3 Surfaces