On the boundedness of some real line arrangements of type at most one
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910012734963712 |
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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 |