Note shows boundedness in line arrangements with intersection multiplicities limited to five, implying few combinatorial types exist.
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 five can have at most 522 lines and consequently there exist only finitely many combinatorial types of such arrangements.
No takes yet. Share an insight, caveat, or question.
Marek Janasz (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: