# Double Points of Free Projective Line Arrangements

1 被引用数 (Scopus)

## 抄録

We prove the Anzis-Tohaneanu conjecture, that is, the Dirac-Motzkin conjecture for supersolvable line arrangements in the projective plane over an arbitrary field of characteristic zero. Moreover, we show that a divisionally free arrangements of lines contain at least one double point that can be regarded as the Sylvester-Gallai theorem for some free arrangements. This is a corollary of a general result that if you add a line to a free projective line arrangement, then that line has to contain at least one double point. Also, we prove some conjectures and one open problems related to supersolvable line arrangements and the number of double points.

本文言語 英語 1811-1824 14 International Mathematics Research Notices 2022 3 https://doi.org/10.1093/imrn/rnaa145 出版済み - 2月 1 2022

• 数学 (全般)

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