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<p>We show that there are only finitely many combinatorial types of free real line arrangements with only double, triple and quadruple intersection points, and we enlist all admissible weak-combinatorics of them. Then we classify all real <i>M</i>-line arrangements. In particular, we show that real <i>M</i>-line arrangements are simplicial.</p>

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On free line arrangements with double, triple and quadruple points

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月4日

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  • Marek Janasz,
  • Izabela Leśniak

摘要

We show that there are only finitely many combinatorial types of free real line arrangements with only double, triple and quadruple intersection points, and we enlist all admissible weak-combinatorics of them. Then we classify all real M-line arrangements. In particular, we show that real M-line arrangements are simplicial.