On the boundedness of some real line arrangements of type at most one

Marek Janasz

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arXiv · 2602.05409

On the boundedness of some real line arrangements of type at most one

Marek Janasz

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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.

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Marek Janasz. 2026-02-05. On the boundedness of some real line arrangements of type at most one. https://arxiv.org/abs/2602.05409

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