Double Points of Free Projective Line Arrangements

Takuro Abe

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1811-1824
Number of pages14
JournalInternational Mathematics Research Notices
Issue number3
Publication statusPublished - Feb 1 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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