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

Fuente: arXiv
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Main Author: Janasz, Marek
Format: Preprint
Published: 2026
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author Janasz, Marek
author_facet Janasz, Marek
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2602_05409
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the boundedness of some real line arrangements of type at most one
Janasz, Marek
Algebraic Geometry
14N20, 52C35, 32S22
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.
title On the boundedness of some real line arrangements of type at most one
topic Algebraic Geometry
14N20, 52C35, 32S22
url https://arxiv.org/abs/2602.05409