2024/01/26 by Lukas Kühne, Kühne, Lukas, Tomasz Szemberg +3
Computer Science · Mathematics · #05B35 #14N20 #52C30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2401.14766
openalex publication_date 2024/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conjecture that suggests the existence of only a finite number of such arrangements, regardless of the characteristic. Leveraging the theory of matroids and employing computer algebra software, we rigorously examine the existence and non-existence across various characteristics of line arrangements with up to 19 lines maximizing the number of triple intersection points.