Affiliation:
1. Institute of Mathematics for Industry, Kyushu University, Fukuoka 819-0395, Japan
Abstract
Abstract
We prove the Anzis–Tohăneanu 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.
Publisher
Oxford University Press (OUP)
Reference22 articles.
1. Roots of characteristic polynomials and and intersection points of line arrangements;Abe;J. Singul.,2014
2. Divisionally free arrangements of hyperplanes;Abe;Invent. Math.,2016
3. Plus-one generated and next to free arrangements of hyperplanes;Abe;Int. Math. Res. Not. IMRN,2018
4. Non-recursive freeness and non-rigidity of plane arrangements;Abe;Discrete Math.,2016
5. On complex supersolvable line arrangements;Abe,2020
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献