On the boundedness of some real line arrangements of type at most one
Abstract
In this note, we show that real line arrangements of type at most one, admitting only intersection points of multiplicity at most five, satisfy certain boundedness properties. In particular, we prove that a free real arrangement of $d$ lines with intersection multiplicities bounded by $5$ can have at most $522$ lines and consequently there exist only finitely many combinatorial types of such arrangements.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Combinatorial Mathematics
Mathematics and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 February 2026
- Document type
- Preprint